If you get a PSP, get custom firmware. Then you can use emulators, misc. applications, and all that jazz in addition to what it can normally do. It's the main reason I bought a PSP in the first place.
The fat PSP is more suited for custom firmware due to 1.5 kernal access, as well as the IR port on the top, and it costs less than the slim anyway. The slim does get TV output, though, a fairly useful feature, and faster loading times in some of the newer UMD games due to having twice the system RAM.
The only real size and weight difference between the fat and slim is they took a metal frame out of the fat design for the slim, and you could do easily remove this frame from your fat psp to meet these specs, anyway, if you actually care.
I don't feel like elaborating today, so just go here if you want learn more about custom firmware and what it can bring you:http://psp-news.dcemu.co.uk/
I will say I am anxiously awaiting the American release of FFVII: Crisis Core, among other official UMD games, as well. The PSP's game selection has improved significantly since its earlier days, which had (in general) been quite terrible.