You should be able to grow just about any shade tolerant plant under the Oak(s). I have many small trees (japanese Maples), Native and Evergreen Azaleas, Gardenias, Hydrangea macrophylla, serrata, arborescens(Annabelle) & some varieties of Oakleaf, many species of Ferns & mosses, Hostas, several species of Trillium & Trout Lilys, Helleborus, Wild Ginger(both native & non-native), Dwarf Crested Iris, Chelone, Toad Lilys, Jacobs Ladder, Jack-in-the-Pulpit(several species), Mayapples (several species), Amsonia tabernaemontana, Atamasco Lilys, Disporopis, spring flowering bulbs and more, growing under mine. It has become really crowded under there.
I often plant in unammended soil, but sometimes ammend with composted ground pine bark or compost. The roots of the Oaks are not a problem, if I encounter one while digging, I move over a foot or two to avoid it. I seldom add fertilizer, only annual applications of compost or leaf mold and when watering, insure thet the entire root system of the trees receive water, The health of the trees are of more concern to me, than the underplantings, which can be easily replaced.
Select some plants you like and give it a try. You might want to wait until the temperatures cool off a little, the plants would appreciate it and it's difficult to do any strenuous work outdoors these days.
Rb

Thanks for the advice. It looks like I have many options as far as what to plant.