Glenmorangie is a great way to start. Especially the madiera cask version.
My personal favorite is Highland Park 12. Not too expensive at around $60. Very smooth and caramel forward.
Highland Park 12 is very good and is my house single malt, if you can find it the 15 year is good as well.
Another favourite is Ben Riach Pedro Ximez, it's finished in spent sherry casks (and Imo damn fine, the sherry finish mellows the peat smoke nicely).
Another good 'starter' is Bruichladdich Rocks, easy drinking and smooth (and not real expensive) ; and is usually easy to find.
Single malt Scotch Whisky is great. IF you check out any Celtic Festivals / Highland Games in your area, some of them have whisky tasting usually led by a distillery/distributor rep, or at least a knowledgeable person.
Also Burns Night is coming up, and lots of places will be getting 'kilted up' and doing Scotch flights.