As Grovian pointed out, tearing the paper around the image instead of cutting it out helps a lot. Leave plenty of room around the image (at least an inch and a half). DO NOT fold the paper and tear along the fold -- the fold WILL show up later. I tear along the edge of a table -- and tear UP and away from the table, with one hand holding the paper firmly in place (move it as you go on larger images).
When pressing, I place clean butcher paper on the bottom of the press, then the garment (if t-shirts, just make sure the collar overhangs the press), then your lightly sprayed image paper, then another piece of clean butcher paper. After the pressing is done, lift off the top butcher paper, then hold the image paper down in the center with your fingernails (or put on an OveGlove) and gently pull back the top edge and then the bottom edge to be sure your image is correct. If it's not, put down another sheet of butcher paper and press for another 25 - 30 seconds. Once you have the timing down, you don't have to do this with every shirt.
When you're happy with the quality of the image, remove the image paper and lay down yet another piece of clean butcher paper over the entire garment. Press for 12 - 15 seconds. This will make the tear lines from your image paper all but invisible. Remove the paper, pull off the t-shirt, and snap it in the air a couple of times.
I stopped using teflon when sublimating shirts. If I need to, I use the Vapor Foam kit (mostly for polos, which I rarely do, and for hoodies). You can either wrap butcher paper around the foam and secure it with heat tape, or just lay down the foam on the press and put your paper over it. The reason I don't like to use teflon sheets or pillows is that I find it leaves a shiny area on the fabric which never goes away.