If you haven't had any whisky from Islay yet, get the Lagavulin 16. Might be a bit expensive though. Ardbeg 10y is, I think, not as good as the Lagavulin but for a price of €36 euro's a liter it's quite a lot cheaper compared to the Lagavulin; and it's a very good whisky on its own anyway. Other Islay whiskies you might want to try are the Laphroaig 10y (hell of a lot of smoke), something from Bowmore (seems to be an aquired taste but I like em) and perhaps the Caol Ila, which I find to be a very subtle whisky with not that much peat.
Talisker is a very good choice as well. But what you also might want to try, sooner or later anyway, is some cask strength whisky. Heck, since I love heavily peated whiskies (Ardbeg, Laphroaig, Lagavulin) the only way I really enjoyed the Caol Ila was when it was at cask strength. You can add water to dilute a cask strength a bit but I quite like them with very little water. Something you'll have to find out for yourself.
Also, if you're going on with the single malts, a good glass helps a lot with nosing the whisky. I used to only have...well, crap glasses, stuff like those little tumblers. Then I switched over to a wine glass, which didn't feel alright but it helped with the nose. After that a couple of Glencairn glasses came with a bottle of Talisker 10y and I really love them.
Anyway, whatever you buy, I doubt it'll be a waste. Even if you don't quite like a certain whisky, it might still grow on you and if you not, well then at least you'll know what you don't like.