All shoots growing from below the graft should be pruned or snapped off as they begin to grow. I have several young oak trees. University studies show keeping the limbs helps to encourage growth and strengthens the trunks. Perhaps it's best to keep the limbs on the trunks as long as possible. They do not have to be removed until they interfere with traffic or necessary tree maintenance.
Gardeners also can remove some lower limbs, then add flower and shrub plantings beneath the trees.
Our home has two large oak trees with no grass. An area that gets more than 25 percent shade makes growing even the shade-tolerant turf difficult. Good green ground covers include Asiatic jasmine, English ivy and mondo grass which is not a true grass. If you want a little color, create clusters of bromeliads or add beds of impatiens and begonias. I have been keeping a small fig tree in a room where it gets limited light but good water and fertilizer.