Jim,
Is there anywhere else you can locate your new vegetable garden? It sounds like a major undertaking just to remove the existing vegetation, much less prepare the soil for planting.
There is a tractor attachment that will break up and bring roots to the surface--it is called a breaker plow, and leaves about 8" deep trenches with huge clods after it passes. However, if you have large pines and oaks adjacent to the plot, you will be fighting feeder roots for the rest of your life! Please consider raised beds--your plot seems more adapted to raised beds than to in-ground planting. The beds don't have to be fancy, but they will save you a lot of effort in the long run. Good luck with your gardening!

Thanks marlingardner; I know the roots are going to be an issue but this is actually our best site near our house. We are literally hacking a farm out of a forrest. We may opt to take out more of the big trees. Will the breaker plow cut most roots? I saw an implement called a pasture reclaimer that was advertised as pulling out roots, etc. Have you heard of this?

If you went to the raised garden, would you put down landscape cloth to keep out the roots? We do hope to have a large garden eventually. Thanks, Jim

Jim,
I think a breaker plow will take care of all but the very biggest roots--perhaps really big roots will just be pulled up, not cut, but then you can have fun with axe! I've never heard of the pasture reclaimer.
I wouldn't bother with landscape cloth under raised beds. Roots are unlikely to intrude in a raised bed. The only damage they might do is using up nutrients and water your plants need.
Persist, and you'll have a vegetable garden that we all will envy!

Plain brown cardboard or a thick layer of newspaper is great for putting over existing vegetation, etc. It will smother everything, then break down. Pile your manure, straw, etc on top of it and leave it for the winter. This is called 'lasagna' gardening because of the layers. Google it and you'll get lots of great information.