Well, technically any yarn can be made into socks, but some won't be able to stand up the wear that socks get. Yarns with a nylon/polyester type component are supposed to be the best. For first socks you might try a worsted or DK weight in any yarn just to get a feel for the pattern.
As for stretching you might try using smaller needles. A tighter gauge is sturdier and is probably less like to stretch.
BTW...I don't wear my socks with shoes either. My wide feet just make it to tight. I could go up a size, but I still have the width issue.