Putting big trees into the side of a slope near a building is not a good idea. Low growing native plants in the slope is good. Low growing native grasses and low growing native suckering shrubs might be good for your slope. Check out the hillside forum for more discussion on this.
Consider the removal of the maple next to the house a good investment. There were some tough storms around here this summer that put trees through a lot of roofs.

If the land slopes away from the house I see no reason why oaks, pine, hickory, red maple etc. would not work and would be a start on a woodland. The use of shrubs and understory trees, ferns and wildflowers would serve to complete your woodland.

You could start developing an oak-based woodland. Oaks generally tolerate tough, dry conditions and the presence of Hemlocks indicates conditions are fine for many types of trees.

You will have some difficult areas under the trees, with dry, shade, but there are plenty of native plants that will grow in your yard.

I'd start by developing a master plan for what you eventually hope to have, then begin implementing your plan a little at a time - mulching some areas to kill the grass, planting a few shrubs, etc. make sure you plan for enough space for your shrubs to grow.

I also live on a wooded, sloping hilltop. A lot of our trees grow at angles N-S. A tree removal expert actually told us they were growing like that to grow toward the sun. Can you believe that? WeÂve had two come down just in the two years weÂve lived here. So I wouldnÂt recommend trees either. Or at least not any that grow over 10 feet tall.

IÂve been looking for groundcovers to prevent erosion too. Everyone recommends "Ivy" or "Liriope Grass". IÂm not a fan of either. Ivy is too common and you have to separate liriope every few years and cut it back before spring. A friend recently gave me what I think is "BabyÂs Tears" (Soleirolia soleirolii). ItÂs an interesting plant; a low-growing, creeping evergreen. Individual strands clump together to form the creeping mat thatÂll drape over most anything. But I couldnÂt tell you what itÂs like to rake leaves out of something like that. Hope this helps, but just keep in mind I'm no pro.

Good example of BabyÂs Tears on a lawn:
http://www.plantsofdisneyland.com/plant-description.cfm?recordID=2212101&plantpic=2212101.jpg

I am curious what the invasive viney things are that you mentioned. There are lots of potential culprits (porcelain berry, asian bittersweet, mile a minute, etc.).
Some low growing native sumacs might also be an option for your slope especially further away from the house.

The hillside (north) generally slopes towards my house. It is higher on the east side of the property, so I get a little water drainage advantage there. When I remove the silver maple I will improve drainage away from the house also. My hemlocks are at the northeast corner. They are a little small for mature hemlocks. My thought on oaks was that maybe they would end up in the small range of their potential height on the slope. The dense-shade maple is east, between two houses. I have done some drainage improvements next to it, and am experimenting with liriope there. I may try mondo grass in that area also. That area is the primary path in and out of the backyard.

Re. trees, I may look into Serviceberry if oaks won't live peacefully.

I grew something called baby tears in California, but it sure needed a lot of water. If it is the same plant I don't think it would survive our occasional snow in Oak Ridge.

The weedy viney things I am constantly fighting are climbing euonymus, puncture vine(very hard to extract), and a vine that has an ivy shaped leaf. I have taken it a couple places and asked advice. One nursery told me to call it bindweed, but it doesn't act like any bindweed I have fought before. On the southwest corner it has almost covered a 15 foot privet, which makes it hard for me to decide which plant to attack. It has sent out woody underground runners into a bed of canna.

I tend to think of sumacs as weedy looking, but locally they do get a nice red color in fall. I will rethink them...

Also of note, no oaks have volunteered on my hillside, and we have enough squirrels some should have. Current tree volunteers are tulip poplar and boxelder. I get a lot of pokeweed. I rather like it, but my neighbors grimace.

Thanks

Hi Kathy003,
have you thought about using ferns, hosta, foamflower, coralbells and carex? These all come in many different colors and sizes. Rhododendron, azalea , bayberry, oakleaf hydrangea and some viburnums would be good shrubs. Other small trees to consider are fringe tree,sourwood, redbud and blackhaw.For a groundcover you could try Allegheny Pachysandra(hard to find) or moss. Could the weedy viney plant be Japanese Hops or woodbine???
Have fun creating your woodland garden!! I use gravel for my woodland path, did use mulch but had to replace it too often.

I don't see why you couldn't use some of the smaller oaks like Blackjack oak. They seldom get large enough to do any major damage. Even with hickories, they grow so slowly it would take over 50 years for them to get really large. You might could even plant some of the smaller pines, like Virginia pine.