Oaks resent much disturbance in their root zone. And then there are the ongoing issues of attempting to establish plants of any size in the very rooty and droughty soil under the canopy. I'd skip the 'large' shrubs and stick with low growing, drought tolerant groundcovers that you can start small and let fill in.

I'm a little worried about that disturbance thing, in fact, because this house came with the special surprise of poison ivy under there and I might have gotten a little enthusiastic about removing it. What should I watch out for? (We did call an arborist who gave it a thumbs up a couple weeks ago, and he'll come back in the spring for another look.)

Anyway, thanks for your response; I probably need to hear this about ten more times before it'll sink into my thick skull. Ground cover and forget it.

Disturbance would include digging large enough planting holes to accommodate larger growing shrubs. Or changing the grade immediately surrounding the tree. Pulling weeds or planting small starts of groundcovers doesn't exactly qualify :-)

I have several large pin oaks, which are in the red oak group. Underneath them are - fothergilla, bottlebrush buckeye, common lilacs, calycanthus, spirea, deutzia, tree peonies, Rosa primula, forsythia, flowering quince, Viburnum plicata, Viburnum carlesii, clematis and Annabelle hydrangea. So pretty much anything you want to plant. Depending on the size and growth habit, the south side may get a fair amount of sun.

Whatever you plant, plant very small plants and let them establish themselves.