I am an avid strength trainer and for most purposes free weights rule and machines drool--but that's not what you asked so I will just address the footwear issue.
The most important thing with footwear for lifting is you want as little cushioning as possible so there is no compression under load. Stay away from cross trainers or running shoes!
Olympic-style lifters and powerlifters use a variety of footwear. Olympic-style lifters wear special weightlifting shoes with a raised heel wedge that is often made of WOOD. For squatting, Powerlifters often use Converse Chuck Taylors (if they use a wide squatting stance and want a flat sole) or combat boots or Olympic weightlifting shoes, if they use a narrower stance and prefer a raised heel). For deadlifting, Chuck Taylors, wrestling shoes, and BALLET SLIPPERS are popular.
In other words, use what works. There would be nothing wrong with using your hiking boots for lifting if they work for you. You may also find that your feet adapt and become conditioned over time, and that arch support from the shoe is not necessary. Just as you are training your legs, you are also training the muscles and connective tissue in your FEET, and taking the stress off your feet with overly supportive footwear will prevent this training effect from taking place.
Hope this helps.