Grim Fandango is my favourite adventure game. Monkey Island 2 probably comes second.
Vampire, I'd play the Monkey Island games in order, unless you have an aversion to old (but still lovely!) graphics and a lack of voices - in which case you could skip straight to Curse and see how you like it. I think you may be able to buy the first three games in a single package.
Escape From Monkey Island is an experience best left until you've played the earlier games, built up some great expectations, and you're all set to have your dreams brutally shattered. (Bleah, it's not that bad I suppose.)