That is an impressive list she gave you for not being an arcade junkie. It has a whole slew of genre with very recent games and early classics. Plus, it includes unMAMEd prototype "Beavis and Butthead" and Dumping Project: Most Wanted "Noah's Ark".
Of the games on the list which are actually playable within MAME, you shouldn't have too much trouble using a four way joystick and a few buttons.
Going down the list:
Frogger
Pac-Mac
Ms. Pac-Man
Donkey Kong
Galaga
Dig Dug
Qbert
Space Invaders
Galaxian
Congo Bongo
The above all used (2way)/4way joysticks with alternating player controls, so no problem here.
Tron would be unplayable with just a 4way, but the trigger and spinner could be simulated with a few buttons.
Joust and Mario Bros. would be fine as long as you didn't do two player games, or if player2 didn't mind using buttons for left and right.
Centipede and Missile Command could be made playable using a joystick, but really need a trackball.
Jungle Hunt and Vanguard need an 8way for full control, but would still be playable with a 4way (same goes for the rest of the 8way games).
For games like ET, which I'm assuming is the 2600 version and not the unfinished arcade prototype, MESS or some other Atari emulator would be needed.