Yeah you have to buy a PSP to play it. PSP systems are the only systems that play UMD's and as far as I know Crisis Core isn't on the PSN. But you'd still need to buy a new console to play it from that too.

I say you should go for it. It's a great game, and there are plenty of other good games for the PSP as well. Plus Dissidia is coming out soon and that's a PSP exclusive too, in case you didn't know.