@
Eldriken doesn't need to play Doomsday against his wife, people. It's possible to play inferior secondary characters that allow newer players to get into the game more.
Matchup numbers aren't the decididng factor here: but execution for the good stuff is.
All of Sinestro's inputs are down forward, or down back. It's one of the best special move designs in the game, for starters. His objective is also simple, keepaway until thy get close, where you can then try out your ofense with safe B1, 2, or anti-air into a combo into more keepaway.
I really don't recommend teaching her Doomsday, because then she'll feel inferior to your Domsday, pretty much forever. I've seen this happen with my friends.
Hawkgirl doesn't need to do long combos, and can rushdown and keepaway effectively with her special moves into more of her special moves, in and out.
Green Lantern because Lantern's might leads into satisfying combos, which make his user feel powerful. Back 1 is a relief.
Batgirl would be decent for teaching vortexes, but so would Sinestro.