Paying a contractor to install a deck or patio will of course not be cheap - how limited is your budget?

If the bare patches under the trees are likely to be run around on a lot those could be surfaced with wood chips. A product in my area even gets marketed as "play area chips".

A teacher I used to work with installed her own deck at her new house which totally amazed me. She has become her own handywoman and does just about everything including tiling a new bath. Not me (much older and more tired-ha), but if you have the will, you can do that. If you want a garden under the trees, check out the shade garden and hosta garden forums for ideas. Hostas , ferns, and other shade tolerant perennials would be lovely. The chips Embothrium mentioned would be fine, too, especially if you have children. For privacy, I would do a mixed shrub/tree border back by the fence. Looks like a terrific lot with lots of possibilities if you love to garden.

If that is ivy in the last photo, I would get rid of it, but be ready to plant or mulch as soon as you do. You don't want to leave it open to erosion. It will take a few years to defeat the ivy.

If you want really specific ideas for plants, let us know your zone and nearest city, so we can make appropriate suggestions for plants!

It looks like, generally, the pictures are of along the back property line. It looks like the existing groundcover is possibly English ivy. Whatever it is, it's probably also in the neighbor's yard, which makes getting rid of it and installing a different groundcover or other plants, almost futile. You need a groundcover in order to have a "lawn" for protecting the ground from erosion and for making it pretty, where there is too much shade or slope for growing grass. It looks, actually, like you've already tried to remove the ivy ... but left lots of sprigs. This will also be futile as it will come right back. I don't get the point of NEEDING a groundcover, already HAVING a groundcover, and then trying to remove it in order to do some unknown thing. It would be better just to get all the weeds and scruffy plants out of it and have a nice, uniform, trouble-free and easy to maintain bed. Mowing could take care of its front edge. Nothing needs to take care of the back edge as it's already in the neighboring yards. Cut it at the base of the trees once per year and keep it weeded. Easy.

Need to remove lower limbs off of trees.

They look like pin oaks. When those are limbed up the next set of branches above the pruning sags down into the previously occupied space below them. So that a body can end up working their way up one of these trees over time trying to produce a space beneath until the only branches left are up near the top.