Welcome to Basenotes Ryan!
Since you're saying you're interested in learning more about higher quality fragrances, is it the price range that makes you want to stay with the drug store offerings? There, I would explore the fragrances by Antonio Banderas. Otherwise, you may have noticed that many drug stores now carry a good selection of designer fragrances too and you could sample from them.
Also, take advantage of the relaxed sampling opportunities at Sephora. You can then get good deals on line for your favorites.
You mentioned Burberry. I would continue to explore that house, as well as Bulgari. I really think those two offer a very good range.