My personal favorites are all from the island of Islay (pronounced EYE-la), just off the southwest coast of Scotland.
Lagavulin (LAGGA-voo-lin), Laphroaig (la-FROIG) and Ardbeg (ARD-beg), are all great, especially on a cold winter night. They're similar to one another in that they're all heavy peat and smoke and sea air. Almost like drinking cold, wet smoke, except you can smell the sea as well. Very different from anything else in Scotland. Flavor is really strong, though unless you get into one of the specialty bottlings, the alcohol content is the same as all of them.
They admittedly can be an acquired taste, and therefore a bit of a reach for beginners, but the reach is worth it. If the regular bottling is just too demanding, Ardbeg makes one called Ardbeg Uigeadail (OOO-gee-dal), which is double-matured in sherry casks, and that takes some of the peat out. Lagavulin makes a double-matured, too. Not sure about Laphroaig.
Talisker (TAL-iss-ker) is from the Isle of Skye and my favorite non-Islay. It has some of the smoke and peat and ocean, but not quite as much as the Islays. Distinguishing factor is a blast of black pepper on the finish.
If I'm going for a softer presentation, say a Speyside, my favorite is Glenmorangie (glen-MAHR-un-jee).
A lot of people swear by Macallan's, but it's not my style. Too sweet. If I want that, I want a good bourbon. To each his own, I guess.
None of this stuff is cheap. But it's sipping whiskey, so you don't mix it with anything except maybe a few drops of water. Point being, you don't slug it back....you sip and savor it. So it takes longer to run through a bottle. So while the initial purchase isn't fun, if you amortize it over the life of the bottle, it isn't nearly so bad.
I like mine on the rocks -- the melting ice supplies the water, and I like it cold. Some think that anything other than straight is blasphemy, but I don't care. I like it the way I like it.
I will offer two things:
First, if you really like your scotch mixed with water or soda, don't waste your money on a single malt -- stick with a good solid blend. Johnnie Walker and Dewar's are fine choices. Monkey Shoulder is an outstanding blend, but a bit harder to find.
With a single malt, you're paying for distinctiveness. If you dilute it with 2-3 ounces of water or soda, you're destroying the very thing you paid extra for.
Second, I personally don't pay for age. With a single malt, the standard aging for most, not all, is 10 years. If you pay for the 15, it's a lot more. If you pay for the 25, it's through the nose. And it isn't all that much better. Maybe not even as good. Definitely has snob appeal, and people will fall all over it. But I promise if you put them side by side in a blind tasting, they won't know.