I would look for a system that is quick to play. I play 4E every other week, but would I want to teach my wife using it, probably not, she'd get bored and distracted waiting for her turn.
If I went with AD&D, combat typically moves quicker and there are classes that are much less complicated to play. I haven't touched the old Basic edition in ages, but I suspect it has the same deal, even simpler.
I'm not looking for an edition war here, just giving my opinion.
I'm surprised no one has suggested Savage Worlds yet. I'm reading it now and I can't imagine it will be that hard to get the hang of.