I’ve never done the printing myself, but I have submitted images to cafepress.com to be printed onto shirts. It sounds like you’ve hit the important points, but also I wanted to mention that if you want your design to have no background (as in, you don’t want the printed area to be a square shape – you want the background parts to be left alone) make sure your image doesn’t have a white background. It’ll have to have no background (represented in photoshop by a checkerboard pattern of white and light gray) and you’ll have to save it as a GIF or PNG (preferably a PNG because GIFs are shitty quality), NOT a JPG.