I'll give you the summery of why to buy each system.
DS (not i unless you really like DSi ware).
So look, the DSi is the newest model, and yes, it's a great system. It's got a lot of upgrades, a camera, and voice recording and all of that. However, if you missed out on the amazing GBA series, then get the DSL. With the combined libraries of the DS and the GBA, you can play for years and never run out of great games to play. It's got a little bit of everything, it has great platformers, great RPGs, a few great racing games, one good shooting game, a few good fighting games, a few good beat up em/side scrolling games, a few good adventures games. It's great.
PSP-
Ok, so the PSP doesn't have as good of a library. Ok, so newer PSP's may never catch on to that awesome homebrew scene it had. There is a lot going against the PSP, but there are some great games too. It's got great visuals, it has some really killer RPGS, it has the really nice Monster Hunter franchise, it's got video and MP3 playback. It has some great games, but you definitely need to do your research first.
Personally I like the DS over the PSP.
PS3:
The PS3 has been slammed, and rightfully so. It's losing exclusives to the cheaper xbox360, and it's really hard justifying the high cost. However, free online, free WiFi is great for the system. It's a great blu-ray player, and it has some great games in LBP, MS4, Killzone, Resistance, SOCOM, and Motorstorm. Of those, you might probably only enjoy LBP and Motorstorm, and even then, that could be a stretch. Other exclusives you could enjoy include Hakuna Matata, and in the future White Knight Story.
Xbox360:
Ok, so it has better exclusives. It's got Halo, Gears, Fable, etc. Exclusives you might like better are Viva Pinata, Dead or Alive 4, Lost Planet, Rumble Roses, Banjo Kazooie, Fable 2, and Project Gotham Racing. The downsides are the paying for online play, and failure rates of the Hardware (i know it might be solved now but we aren't even like 2 years into the Falcon, lets give it a bit before we call it mission accomplished). It's a great system for this generation right now.
PS2:
Oh goodness what a great library it has. I mean wow. It's got a lot of RPGs, a few good fighters, the GTA series as an exclusive, and a crapload of games. I mean seriously. If you really just wanted an endless amount of games to play go get a PS2. If you want a next gen experience go for the Xbox360.
If you want, I can give you an overview of the Wii and why it could be a good option for you, but I noticed that you didn't put it on your list, so I won't. If you want me to however, just ask.