I got this unknown tree in the Fall. It was a massive rootball, two feet wide X 3 feet long and 20 inches deep, and that was the left over piece. The other part was 3 times larger.  It was brought from Italy about 60 years ago. Not sure which region. The reason it was being removed was because the guy who bought the house ate 6 figs and found out he was allergic to them. Since he has a small yard he didn't want anything there that he couldn't eat, so out it came and I just happened upon it. It has green figs with a pink/red center. The question is do I let it grow unchecked this year and then start to shape it next year or should I thin it out now and shape it now? I'm going to cover it for winter since that's how it has been taken care of since it was planted decades ago.

That's a real nice  looking tree.  If it was me, I would wait to prune it till it goes dormant.  

I'd wait to prune it. If nothing else you'd have cuttings to trade or give away :-)

Maybe that would be the best thing to do. I'll most definitely have some cuttings to trade/give away. I do have some trees started already. I'll keep one for a backup. There's no figs on the inground tree, which is disappointing. I thought there would be a few, but since it's a new transplant it probably needs to regrow some roots. The guy who originally had it, cut it down to the ground and threw most of the branches away before I got there. The branches that were left in a pile were loaded with unripened figs. If he could of only waited 2 more weeks they would of been ripe. What a waste :(