Some good ones mentioned already and it will of course come down to what tastes good to you.
Some of the popular Islay pours don't taste very good to me. Glenlivet Nadurra etc.
Good places to start:
Highland Park ( Dark Origins, if you can find it, is one of the best I've ever had )
Lagavulin 16+ years (younger has a harsher bite which doesn't work with the peet IMO)
Bruichladdich (outstanding and not hype priced)
Laphroaig has some good batches and some not so good
bunnahabhain 25 is phenomenal if you can find a good price on it but at that price point it will never be a daily for most
Look into whiskey tasting clubs in your area. I joined one a few years ago and it's been a great way to sample a LOT of different scotches, help build your taste preference profile etc.
My regular scotch is
Glenmorangie 18. Not an Islay but has incredible flavor and smoothness without the crazy price tag.
Scott