Go to a thrift shop or salvation army store and pick up a heavy leather jacket, a sweatshirt and a t-shirt. Wrap these around a plastic gallon jug of water in the order you would normally wear them. Step off ten paces and shoot at it from that distance, with #6 birdshot. This would represent a probably home invader in Ohio in winter.
I think you will be underwhelmed with the results.
If you are super worried about over penetration, find some of those rubber ball or bean bag specialty shotshells. I'd load up 2 rounds followed by a bunch of #4 Buck. Then practice 2 VERY quick shots with a short pause to evaluate the situation before you follow up with 2 VERY quick shots of Buck.
As said, the minimum acceptible standard for self defense is #4 Buck. In leiu of that, I might be persueded to drop to T, BBB or BB, but only as a stop gap measure.