UPDATED THE LIST :0!!
I like Nintendo related stuff, Chocobos, Futurama, Space Invaders and some other "retro" ones (as they like to call them), Videogames overall (though I'm not much of a fan of war games and FPS games), Red and White (as colors), Video Game Bosses (I have this thing for evil characters heh), Toys and Vinyl toys, collecting things, Chameleons, Snakes and Turtles, and uhmm that's all I can think of right now.
do the gifts have to fit inside the box we're assigned?
Not really, they are just for hyperlinking your gift and make the whole present opening more realistic; so your gift can be any size you want.
Just pick whichever gift wrap you like or think that will fit your partner the best, even if someone else already chose it.
Does it have to be really good?
I'd say try your best. But would you be happy receiving something with the quality of the picture you did?.
If yes, all good. If not, maybe you should work on it more.