I am far from an authority, being new to single malt tasting myself, but happy to share what I have learned thus far, applicable to your question.
You will probably want to avoid the Islay and Island malts in general. They are most likely to be peaty/smoky (and a bit briny). At the other end of the spectrum are the Speysides, which tend toward sweet and not peaty at all.
In between are the Highland malts (my favorites so far). Dalwhinnie 15 is one such, with just a hint of peat and smoke, not too sweet and very smooth. The Dalmore is another. I am now enjoying a 12-year-old, but they also offer longer-aged bottlings well within your stated price range. Again, slightly sweet, no peat or smoke and delightfully smooth and drinkable.
Sample-size bottles and tasting events can save you from buying an expensive bottle of something not to your taste.
Enjoy the quest!