Not much of a PSP expert, but I've had all 3 versions (1000, 2000, 3000). Allegedly the 3000 had some ghosting issues, which to my knowledge occured during your more fast paced games. I never noticed any ghosting on mine while gaming, but when I watched movies (probably due to the fact that I wasn't concentrating on one small piece of the screen, but rather the whole thing) it was noticeable. If you check the deal forum I think there's a PSP1000 deal at gamestop for 99.99 used, but you'll have to double check that. The 1000 had dead pixel issues ( I had one with a few dead pixels when it first came out).
As for mods, I think the 3000 was just cracked, but I never used the mod/homebrew thing considering it's not only illegal, but I'm from the school that if I wanted to play super mario on a portable I'd have a gameboy, but that's just me. I'm a cheap ass gamer not a pirate ass gamer, so you're on your own for that. The 1000 also had some button issues, with the "square" button sticking because of the design of the psp. I know people who swear by the 2000 considering the 3000 has ghosting issues, and few if any had dead pixels. I do know that the new psp is slated to drop, and won't have a a UMD drive, so your UMDs will be useless until Sony figures how to swap your library for digital copies (which will be VERY interesting to see in action). Your PS3 will be very handy for downloading PSN stuff (i.e. FFVII) and transferring it the PSP.
As for price drops, at E3 Sony said the 3000 will stay on shelves beside the new PSP, so I don't know what will happen with a price drop once the new system hits. I do know, that RadioShack, and Dell have had the PSP models on sale over the past couple of months, and that may or may not be an indicator of what's to come. Just keep your eyes peeled.
As for other games, God of War chains of olympus was great, but it was way too short, FF Tactics wasn't bad if that's your thing, and FF Crisis Core was fun, but I personally downloaded from PSN more than I used UMDs. As for essentials you'll need the USB to Mini to link your PSP, but your PS3 controller cable USB cord will double, you'll probably want some form of case too, considering the screen will take a beating in your pocket since its not clamshell. You'll also need some memory, I always used 2 gb sticks, but every game takes up different space for saving and downloading. Like FFVII took a little over a gig, while Tekken 2 used roughly 500 mb. Hope I helped a little, PM or post if you've got other questions.