Pecans do very well here. I would get some fig trees, too. Celeste and Turkey Brown are good varieties. Peaches actually do well here, too.

Personally, if I was starting with a woody lot and didn't plan on doing a lot of clearcutting, I'd concentrate on something different than nut trees (which tend to grow big, need full sun, and often require spraying and maintenance). Pawpaws are one type of fruit tree that will do well in the shade. If you grow pawpaws, you could start them off in a semi-shade area and then clear a little bit of canopy away in a few years to introduce more sun and increase fruiting. There are actually quite a few edible fruiting plants that will do OK in light shade.

Yes, pawpaws will grow in the shade, and yes, they will fruit - albeit quite lightly - in the shade, but if you really want fruiting in any substantial amount, they need to be grown in full sun. And, despite all the positive press coverage they've received over the past 15 years or so, in my experience, most people who've had the opportunity to sample them don't care for the fruit - its consistency, flavor, or aroma. I wouldn't recommend anyone go wild planting them unless they know they're one of the folks who don't find them disgustingly insipid.

The OP doesn't state where they're located, though I have to suspect somewhere close to or in TN, since they've listed this forum as one of their faves.
If you truly are in zone 7, and committed to pecans, I'd look at some of the selections that have been recommended for home and low-input planting(see the link below). If you're really more of a hot zone 6, some of the Northern pecan selections, like those originating in KY, MO, KS, IN, etc. may be a better choice. And, yes, you'll have to remove some forest cover to accomodate them.

Here is a link that might be useful: Pecans for Home/Low-Input planting

On the nut tree front - don't discount hickories; they're worthy of cultivating.
Check out the nice recent article linked below, for more info.

Here is a link that might be useful: Consider Shagbark & Shellbark Hickories

I've seen, I guess, the opposite reaction to pawpaws. While some people don't care for them, I think more than half actually like them, and many like them a lot. Many people actually hate pears, but like with pawpaws, it's just a matter of personal tastes and has a lot to do with what kind you get. Many pawpaw cultivars have a much better taste (and aftertaste) than the average wild pawpaw. Also, some people prefer their pawpaws a little cooler than freshly picked and at outside temperature. No fruit is going to be everyone's favorite, so if we eliminated all of them that not everyone liked, we'd be left with nothing. Pawpaws don't store/ship well, so that's why they are less common in grocery stores. However, where they are offered fresh, they are often quite popular.

Pawpaws do fruit much better in at least a mostly sunny spot (hence the comment in my first post), but do best when provided some shade in their first few years (most pawpaws are planted when relatively small because of their taproot). Also, one pawpaw can produce a considerable amount of fruit in full sun. The homeowner with two or three trees probably wouldn't need that much fruit and so wouldn't necessarily need full sun trees. Pecans, and most nut trees, are going to require a LOT more open space (ie full sun) than pawpaws.

To sum up my thoughts, think outside the box and consider working with what you have (more shade/semi-shade than full sun). There are lots of choices, and it's worth taking the time to consider many of them.

I'm in Knoxville, Tn.

...and I'm loving these responses. Thanks.

I need to try one of those Paw Paw's, too. In fact, I think their might be one on the property. When do they fruit?

You should have little baby fruit on them now if yours are going to produce this year. Generally, you need two different trees for pollination, but some cultivars are somewhat self-fertile.

Walnut apparently does well here to. I have several on our property and a huge pecan. Course we just moved here as well and still getting a feel for this zone.We planted apple pear and peach, hoping they do well. Good luck with your trees!

I wouldn't put much stock in planting black walnuts in this area right now. From what I've heard, the thousand cankers disease is expected to become a significant problem.

Here is a link that might be useful: Thousand Cankers Disease