The only time I use intefacing on my T-Shirt quilts is if the fabric is very flimsy. Otherwise I just use them as is. Mine are also different than many by having multiple sizes cut. I use the method that Too Cool T-shirt quilts uses. Pieces are cut in increments of 4 inches (plus seam allowance) based on the design on that shirt. Pieces range from 4in X 4 in to 16X16. This will include non-square pieces also - 4X8, 4X12 etc.This makes for a very interesting T-shirt quilt. I then plan the layout based on shapes, sizes and colors of cut pieces. I will typically add a quilting cotton border and backing.
As for quilting, I machine quilt on my domestic machine usually using invisible thread on the top. I do not typically quilt through any designs because the designs sometimes 'grab' the needle. I will outline quilt the design and letters (or the word if the letters are small) and then do some type of background quilting in the rest of the block. My background quilting usually varies from block to block.