For your first try, I would recommend going to a decently-stocked bar on a night it's not too busy, tell the bartender you want to try a few different single malts, and ask him (or her) if he (or she) would let you pay for one drink and try small doses of a few different scotches. This way you can find one you like before you buy a whole bottle.
Good starters, IMO, are Glenlivet and Glenfiddich (both very easy-drinking, not too strong or one-dimensional).
Balvenie doublewood and Cragganmore are also very nice, but may be harder to find at a bar and cost a bit more.
Highland Park is good and will give a bit more of the smoky/peaty flavor than those above.
If you do go this route, and like what you've tried, you might consider trying an Islay malt (Laphroaig, Bowmore, Lagavulin, Caol Ila, etc., just tell the barkeep "Islay" (pronounced eye'-luh)) just for fun. As has been said above, the chances of you liking it are probably slim. I was one of those that did like the flavor profile immediately, but it's a well-known fact that I'm a nut-job.
You could also try some of the better blends. IMHO, single malts are not always better than blends, just different, and I drink plenty of blended scotch. Good blends include Dewar's 12 year old (standard Dewar's white label is just OK), Pinch Dimple, Chivas Regal, and JW Black.
And, if you've already tried some, Loyd, how did it go?
