Intrigue is in my opinion the one with the most interesting and fun cards, and I only have the first edition with a couple of duds, but it's still awesome and the experience with Intrigue turned Dominion from a game among others to the game above all other. That said, Hinterlands is not bad either. It's simpler and that is a good thing when playing IRL, also a star you should absolutely get as soon as you can manage.
Alchemy you can wait with, the cards are actually great but unfortunately they are a bit of a pain to resolve IRL and we stopped playing Alchemy pretty quickly after the novelty ran off. I don't want to bash it further though, because the potion mechanic is so interesting, but prioritise the other two, that is what almost everyone would suggest I think.