Knit a backing? I think that might be really, really thick and heavy unless you're using a lace or fingering weight yarn, but maybe that's just me.
Personally, I'd probably do whatever I could to make it all in one piece. You can even create a look of blocks that way. Here's a few ideas. (Ravelry is free to join)
If you have your heart set on making squares and seaming them though go for it. If you practice a bit first like I suggested I'm sure it'll be beautiful.