Verified answer

To start off, I would suggest getting Super Mario All Stars which have a bundle of mario games in it.

For others, I strongly suggest Final Fantasy II, Kirby Superstar, Mortal Kombat (or Streetfighter), R-Type, Harvest Moon, Link to the Past, Super Metroid, DK, and Mega Man!

Can't find those all just try to get All Stars, FFII, Link to the Past, and Donkey Kong. Great starting offers. =)

Chrono Trigger

Super mario world

Zelda: A link to the past

Super metroid

Donkey kong country

Earthbound

Buy all of these now

Super Mario RPG

Secret of Mana

Secret of Evermore

ChronoTrigger

Final Fantasy 6 (3 in the US).

Arcana

Any Might and Magic game.