I'm new to basenotes as well, but I'm not new to fragrance. Unfortunately I'm an older guy so I'm not sure how much help any advice I give you will be. That said, I do have something of a fetish for cheap-but-nice perfume. Much will depend on where you live. I find that in Australia the only way to get a good deal is online, but this is nice because I can buy scents like Caron which are incredibly rare here and get a niche effect for a very good price. Thus I save my money to stock up on vintage scents I really dig. Patou, Worth, Givenchy, etc.
It's summer on your side of the world, yes? You could try Yuzu Man by Caron. It doesn't have much praise on BN and I don't wear it myself but then I'm more than twice your age, and also we're still a few weeks off spring on this side of the world; it is well-blended, and a good scent so far as those light, summery things are concerned. Also I doubt anyone your age will be wearing it. It may be difficult to find though. Another nice scent for summer worth considering is Givenchy Into the Blue. It's one of the only aquatics I can handle, but my SO keeps stealing my vapo so I don't get to wear it much, but the 'travel size,' 50ml vapo could be handy for someone experimenting as you can take it with you and freshen up throughout the day. Mine was under $30
CK's IN2U might make for cost-effective summer scent, but I don't think it lasts long enough personally. I'd take Cool Water over it myself, but some have said it's one of CKs better masculine fragrances, and I've been known to spritz my bed sheets or open curtains with it.
Kenzo's Jungle Pour Homme could work as an exotic summer scent. It has a super-cool bottle too, but costs a little more than the others I have mentioned. If you're feeling adventurous maybe consider a split or smaller bottle of Citrico from CDG's Cologne series, or perhaps Vetyveru. I've seen the smaller bottles for reasonable prices, but the longevity could be an issue so this might not be a safe buy for someone pulling together his first few bottles. CDG have an arty rep, but the cologne series is probably their most wearable, and affordable.
If you ever get those ice-cold summer nights where you live, or you want something handy for when the seasons turn a 75ml vapo of Joop! Homme can be had for a tiny sum, and those 75ml's will last you for 75 lifetimes. This bright pink bottle is full of some loud, loud, loud juice, and I think it's fantastic although others disagree. It might be a little daring for someone your age, but if you're soft on the trigger and spritz yourself ten-fifteen minutes before heading out you could make a big splash - this one has been known to do strange things to women. Oh some people might look at you as if you're wearing a live octopus on your head, but for others this wonderfully inexpensive stuff is human catnip.
4711 - classic, bracing cologne. Very good price, splash it around and enjoy yourself.
Mandarina Duck Pure Black - a rare gem among modern scents. May be at the top-end of your price range, but this one seems to bring a lot of compliments and is quite versatile, plus the longevity is wonderful. The strong orange note in the opening turns some off, but I find it wonderful as to my nose it is very natural whereas most orange accords seem too synthetic. The bottle is cool too, reminds me of my funky old Xeryus vapos. Girls really seem to like it.
Worth Pour Homme - the modern iteration is a little watery and lacks projection and staying power, but if you carry an atomiser you can freshen up during the day. It is one of the most fabulous scents for the price. At $15 or thereabouts it is a very classy fragrance, and probably no less troublesome, longevity-wise, than the current cool water. Perhaps a little 'old,' for you, and maybe more suitable for cooler weather, but I think you need to know that it's out there, a classic for under $20 that puts a lot of fragrances three, four and five times the price to shame.
Lanvin Vetyver - can be had for under $20. Yes, it takes a lot of heat for butchering a classic (the original Vetyver was very different) but taken on its own it is a nice, inoffensive green scent. The modernization makes it more wearable for a younger man. Lanvin l'homme may also be worth checking out as an inexpensive compliment generator. Personally I could never own just one of these two simply because they look so nice sitting side-by-side in their lovely little blue-and-green bottles. There are other Lanvin masculines which are equally inexpensive, but you'll need to check the reviews yourself as they're outside my sphere of interest.
Grey Flannel by Geoffrey Beene - I recently bought a fresh bottle for $12. A slightly dandy fragrance with a bitter fruity opening and a pleasant fade to sharp wood and moss. Dated yes, but then so am I. Probably not for a young man, but who knows?
Azzaro Pour Homme is another cheap classic I dig, but again it might be a little old for you. Explore some other Azzaro fragrances though (Azzaro Chrome, someone mentioned earlier?) I'm not familiar with them, but theyre affordable.
Caron's gentlemanly Pour un Homme, gorgeous Le 3me Homme, edgy L'Anarchiste and beastly Yatagan are all worth sampling. It may be that these are too mature for you, but it has been said before in this thread there are no rules. I have always liked mature scents and wore Givenchy Gentleman in my youth, and this was the old GG which was an insane powerhouse. Yatagan at least will certainly get you noticed, it's a savage beast of a fragrance, but a classic all the same. Le 3me Homme is one of my all-time favourites, but some find it a little too floral and feminine, I do not think this is the case at all. Caron Pour un Homme is a time capsule, but a good one, a real sophisticated gentlemans scent and L'Anarchiste is something that will set you well apart from the crowd plus if you like nice bottles this one is a must. All can be had for under $35 and in very good sized vapos too.
Khiel's Original Musk - dated as all heck, but terribly fun. The oil seems a little pricey where I live, but one can buy it in a smaller roll-on form for a bargain.
Tabac Original - this one has a sore reputation, and can be (hilariously) inexpensive. I recently purchased a gigantic 300ml flacon for under $20. Like 4711 its great to have something pleasant you can splash around with abandon; as far as cheap colognes go I rate it above 4711 but then it is more of a fragrance, and not quite as bracing as a cologne perhaps should be. I say this as the eau du cologne is said to be the superior scent, and quite different to the eau du toilette. Shop around, test, and take care. I've come across EDT's which boasted a gorgeous leathery, tobacco accord while others claim this one is more floral so perhaps I was sampling some old shelf stock? The shaving soap is good stuff too; I shave with a Kamisori and it does the trick where others fail.
That's as much advice on individual scents as I'll give tonight. I hope some of it helps. Beyond that though if you want to start a fragrance collection and you can't afford to throw money around there are many ways to do so on a budget.
The internet is a good place to find cheap fragrances, but always keep postage in mind. In my experience it works best when buying bulk as this helps to limit the postage costs, but this may not be feasible for you. Still it is a good place on which to look for bargains. One of my local pharmacies has a good perfume selection and often runs 'in store only,' specials. Some of these are very, very good! I check the website every now and then to see what's shaking. There are also many online resources which allow you to compare the price from many different vendors for a single product, and this can be very helpful.
Get yourself a couple of atomisers. These can be had for quite cheap online, but if you can find one over the counter all the better as quality can be an issue. You can use a straw (dispose of after use, use a new one each time and make certain it is clean) or spring for a small hand siphon or an eyedropper (though it will need to be washed properly after use, I use ethanol but cheaper options exist) to decant your fragrances. This can save you a great deal, and is quite handy. You can decant from splash bottles (which are often cheaper) as they are difficult to use without waste. Further the solution to many a longevity problem is to apply a fragrance to fabric (though some may argue that this limits the experience: you must decide for yourself) and this is difficult with a splash bottle. A small atomiser can be carried in ones pocket and used to freshen up as well and this allows some cheap classics like Worth Pour Homme to come into their own. Plus if you ever buy a fragrance which has longevity issues due to your skin chemistry then it need not be pushed to the back of your shelf and forgotten.
Also if you grow to love a scent which exists only in an eau du cologne form (like something from CDG's cologne series, for example) a pocket-size atomiser may be the only way to carry the scent all day.
Moreover some pricey scents that you may wish to try in time, such as Eau Savage or my beloved Givenchy Gentleman (vintage) can be purchased in a much-diluted aftershave form for far less. Such a bottle can be a viable scent if you are able to reapply on the fly, and this might allow you to experience some more pricey fragrances on a budget. That said vintage GG aftershave lotion is stronger than many modern EDTs, which is a little tragic.
Splits and decants are a great way to save money. Online transactions might seem risky, but keep in mind that at least when it comes to splits it might be worth talking to friends. Of course there are those who (like me) think the bottle is half the fun, and if you feel that way don't cheat yourself. I know if I had bought something like Jungle Pour Homme or VC&A's Midnight in Paris as a decant, or split in a simple glass atomiser it would only irritate me. Still even if you feel this way there are some brands or series (like Annick Goutal) which, while containing fragrances of note are of little value to one who covets interesting bottles once you have one. If you go splits with a friend it might be worth making some sort of schedule though so you don't end up wearing the same fragrance at the same time.
I've been told that a light application of baby oil (in fact any lightly or unscented, natural base oil works) to the skin at each of the points you wish to apply fragrance to can enhance longevity. I've tried this, but my skin is very fussy so I've met with mixed results. I know people who swear by it though and have experienced it at work. A large bottle of baby oil will only set you back a dollar or two so there isn't much to loose. You can also use it as a perfectly serviceable pre-shave oil to soften hair and help with lubrication, but I would not recommend such extensive use as it is not especially good for your skin.
Old shelf stock can sometimes lead to amazing discoveries. Only recently I found pre 2000 bottles of Guerlains Vetiver and MDM and purchased them on sale for less than retail. Testers can be had for bargain prices too, especially if they have been used. Some testers have a superior atomiser to the normal retail bottle, which is a bonus. If the partly-used bottles arent for sale dont be afraid to make an offer. This can work wonders at privately owned outlets. Furthermore samples, minis and so on should not be overlooked. Free 2ml samples can be had at many department stores, or purchased online for a few dollars including postage, while minis can really help when one has to make a difficult choice. Those sample packs, which the likes of Dior and CK sell allow one to really get a feel for a few different fragrances for a very fair price.
Lastly bear in mind your needs, and do not fall into the trap of buying too much or too little. Many scents come in a wide range of sizes from tiny 2ml samples up to giant flacons. Sample. Test. Take your time. Really think about your purchases. Unless youre collecting for the joy of it try to think how each particular fragrance will fit into your collection. Are you going to be dousing yourself in it daily, or wearing it only on special occasions? Will you need to carry an atomiser to top-up every few hours? Do you need to use a lot, or is this a powerhouse scent where a light spritz can last all day? Buy a decidedly cool weather scent in the height of summer, or vice-versa and it might sit on your shelf for four months before you get to use it, and next week you might stumble on a winter scent you can wear right now which you desperately want. Samples and minis are great to pick up when you're feeling impulsive and daring, less so full bottles.
I hope some of that advice helps. Also if a more experienced Basenotes member can give me some info on sending fragrances internationally (the few times I've tried there have been issues) I can send you a decant or two of the fragrances mentioned above if youd like to pick a couple, or - if you like - something a little more special such as some vintage GG or Worth Pour Homme (vintage blue bottle, or haute concentration) as I have some little atomisers handy which are 15 or 20ml.