I always heard the praise too and couldn't really understand it. But then I only know the hits and some of them are good (but not what I would expect from a "genius") and some of them I don't like (Kiss is an annoying tune imo).
Is there an album that represents him best? What would be a good starting point if I wanted to try to get into his music?
I'm not a hard core fan, and I'm sure there are hits packages or something that are better, but IN MY OPINION, you start with Purple Rain. It's his Thriller; to say "yeah, I'm familiar with MJ", you have to have heard "Thriller" and for Prince it is the same thing.
Here's the thing, though: his "greatness" was often very subtle. I don't mean that in terms of hipster "you don't get it", I mean in terms of... a good portion Purple Rain is actually live, with studio overdubs, not unlike Starless and Bible Black by Crimson. He was just one of those guys that knew what he wanted the final product to sound like and knew how to get that. It wasn't "songcraft with Desmond Child", it was "I have a muse, and I'ma going to follow it, motherfucker". There's an integrity to his process that I think gets ignored (or isn't even known) by the casual fans. I think it wasn't until his fourth album that he had any significant outside contribution from ANY other musician (I know on his second album, he wrote and played every single note, sound, tone, etc. save for a passing harmony vocal on one song). Aside from some horrendous album covers on those first four records, that's where he made his name.
I think one of the greatest things I've ever heard about him was: the record company wanted a hits package and he said no, and won the argument, releasing "Diamonds and Pearls" instead. A year or so later, the record company wanted a hits package again, and he said no, so they actually PAID him to NOT get involved in it. I think that is so cool.