Assuming it isn't a southern "live oak", with which I have no experience garden-wise, there are lots of things (nice things) that will grow in the dappled shade of an oak tree, which is often considered dry shade, as the oak is going to take up the lion's share of any water.

It would help a lot to know where you live, what type of soil you have (sandy, clay, or the gardener's dream: a rich loam with lots of organic matter) and whether the trees have been limbed up or not. If they have not been limbed up, the removal of some of the lower branches will allow more light into the area beneath, also, judicious pruning by a qualified arborist might open up the canopy to allow more light through.

If the ivy is English or Boston ivy, get rid of it. Don't feel guilty about it, just do it. Both have been declared invasive species in many regions of the U.S.

Since you're out of town a lot, you'll want low maintenance. Depending on the size of the area and your taste, you could put in a mix of understory shrubs, perennials, and maybe a few naturalizing spring bulbs for early color. (By the time the oak canopy has filled out, the bulb foliage will have gotten all the sun it needs for next year's bloom.) I lean towards native plants for several reasons, but important here is that they are usually low-maintenance, as they have evolved to be suited to the local environmental conditions. There are also many non-native species that would be good neighbors for your oak trees. Without knowing your region or site conditions, however, I would not venture to make any recommendations.

Most of my gardens spend at least some time in the shade of trees in this neighborhood, mostly oaks: white, red, pin, chestnut. It presents a challenge at times, but the movement of the dappled sunlight across the understory plantings adds a delightful dimension to the garden.

Hosta. Lots of varieties, but be careful. One tends to become addicted. Head over to the Hosta forum and see!

bed full of hostas and nothing else = monoculture
monoculture = increased susceptibility to pests and diseases

also, imho, boring there are some nice varieties, but make it interesting and show them to their best advantage by mixing them with some other shade-lovers like ferns, fern-leaf bleeding heart, astilbe, primrose, maybe a young flowering shrub or two.

think about all four seasons - what will be there? do you want to look at bare earth half the year? if not, be sure to include something that will provide winter interest - either evergreen groundcover or shrubs or deciduous shrubs with an interesting bark that will be revealed in winter.

when/if planting anything below the oaks, be careful of their roots - try to plant between them rather than disturb them. smaller, younger plants with smaller root balls will be easier to tuck in here and there.

tiarella is one of my "go to" plants for dry shade. so many varieties, spreads politely to form a ground cover, bloom season about 6 weeks, and native to our region.

take a loot at Mt. Cuba Center's website below for inspiration using native plants in sunny and shady sites, and if you're of a mind to visit, it is well worth it ... i can't wait to go back.

Here is a link that might be useful: Mt. Cuba Center

Yes, I agree that a mix of shade plants is lovely and I include all those mentioned plus heuchera, hydrangea (especially like the H. paniculata 'Tardiva'), Sweet Woodruff, brunnera, native ginger, etc. i also have spots that are all hosta.

Have to say that a bed of hosta does not have to be boring-the pic is from the AHS. :)

Here is a timely link about companion plants that you might enjoy. Lots of pics which is always fun! :)

Here is a link that might be useful: companion shade plants

Let us know where you live. It will be easier for us to offer appropriate suggestions. Planting something now might not be the best thing to do in certain parts of the country.

Jim