Dalwhinnie is a great starting single-malt scotch. Very mild.
I echo the comment on Oban - an excellent scotch and fairly mild. Peatier than Dalwhinnie, but still mild enough for most. Very smooth. If you're into peaty scotches - and I am - then you need to try Talisker. It is probably my favorite scotch. When I'm drinking with others it is Oban, but if I can have what I want I go with Talisker. Unlike tklawg, I like Laphroiag. And for the record, it is not at peaty as Talisker. If you want to impress your guests with your "motor oil", go with Talisker. Also on the very-worthwhile list is Lagavulin. That's a really nice one as well.
I'm currently about halfway done with a bottle of Cragganmore. I rank that one behind Talisker, Oban, and Lagavulin. I've got a bottle of Glenkinchie after that one to give a whirl. We'll see.