Thinking of buying a DS Lite

I'd say go for it. From what you described, it seems as though the DS would be perfect for you. It is really a great system with really good games of the types you say. Besides not having extra features like music and stuff which you already sayed you don't care for, and being a generation behind the PSP in terms of graphics, the DS beats the PSP hands down. Although I do not own a PSP, it seems as though the DS has better quality games and an even larger variety of games. The touch screen and dual screens give the DS the ability to make really unique games that could not have been made on any other system.

Games I suggest for you:

Zelda: Phantom Hourglass (action adventure)

Super Mario 64 DS (platformer)

Elite Beat agents (music)

Mario Kart DS (kart racing)

New Super Mario Bros. and Yoshi's Island (platformer)

Advance Wars: Dual Strike (strategy)

Castlevania: DoS, and PoR (platformer)

good luck!

The bundle really is great. I always use the case and the metallic crimson and black DS looks awesome. Elite Beat Agents is a really fun music/rhythm game. For platformers there are plaenty like DK: Jungle Climber, New Super Mario Bros, and Yoshis Island. For RPG there are a lot too like Pokemon Diamond/Pearl, Final Fantasy 3, FF4 is coming out too along with Dragon Quest games too. Some good puzzle games are Brain Age 1 and 2, Tetris DS, Meteos, the Phoenix Wright games are sort of like a more story oriented puzzler. And then there is Zelda which has puzzles, adventure, and RPG elements to it so you honestly can't go wrong. :D

Edit: I can't believe I forgot Mariokart DS! That game is a must have.

MEGA edit: Metroid Prime Huntrers is really fun too even if it is mostly because of the multiplayer. But you can play against computers in multiplayermode too though.