Um, let's see. I started with Ficciones (http://www.amazon.com/Ficciones-English-Translation-Jorge-Borges/dp/0802130305/ref=pd_bbs_2/002-9751280-1690410?ie=UTF8&s=books&qid=1176673428&sr=1-2), which has almost all of my favorites of his short fiction, but Labyrinths (http://www.amazon.com/Labyrinths-Selected-Writings-Directions-Paperbook/dp/0811200124/ref=pd_bxgy_b_text_b/002-9751280-1690410?ie=UTF8&qid=1176673428&sr=1-2) is supposed to be a better place to start. Since you know you like this style of writing, you might also consider starting with Collected Fictions (http://www.amazon.com/Fictions-Penguin-Modern-Classics-Borges/dp/0141183845/ref=pd_bbs_1/002-9751280-1690410?ie=UTF8&s=books&qid=1176681364&sr=1-1), which has a new translation by Andrew Hurley that is very good. (I still like the original Ficciones translation, though this is really one of those things where you have to sort of feel around for what you like. And, in any case, of course I'm attached to the original translation - it's the first one I read.)

If you can read any Spanish at all, it might be worth getting a Spanish-language copy; I'm considering doing that myself, since Borges is supposed to be pretty easy to read in the original.