I make a lot of T shirt quilts for customers. I found that I like a really light weight interfacing to back my T shirts. Then I either use a really thin polyester or my regular 50/50 Warm batting. Either works great. For a backing, I use a good cotton or flannel.
Remember these quilts are going to get a lot of use so be sure and use a good quality fabric for your backing.
My favorite way of quilting the T shirts quilts is just an all over meander. Very sturdy and looks nice.
Good luck. T shirt quilts are wonderful.