Good games to spend time with

Gameboy Advance: Pokémon Fire Red/Leaf Green and Pokémon Ruby/Sapphire/Emerald. Those were the games of my childhood :). Still the best Pokémon games to-date

crash tag team racing, pokemon games, wwe....etc.

Monster hunter series for PSP, Gameboy: metroid fusion

this might help .

Beginner: "Final Fantasy tactics advance" on GBA
Once you finished that, then you can play: "Tactics Ogre" on PSP (much harder ver)

EDIT:
Forgot to mention that it is "Final fantasy tactics advance", not final fantasy tactics

Golden Sun & Golden Sun 2 - musthave rpg for GBA!

Monster hunter for the PSP, each quest will be a max of 50 min or less depending on your skill level so it'll roughly be your amount of waiting.

Patapon - I don't know if it's a game you're looking for, but anyway, it's a must-have for PSP imo. ;) But you must have good earphones for it.

I would also recommend a Monster Hunter series, but you said earlier that it's not your type of game.

And for Gameboy - Pokemons of course. ;)

Fire Emblem is also great on Gameboy Advance.

Hm, for the GBA? Beside the Pokemon Games (which by the way are also RPGs) I would recommand "Fire Emblem 7". I think it is Rekka no Ken, but I'm not too sure. There are only two for the GBA and they are both good.