I ended up holding the yarn doubled for the top part and did a garter stitch edge. Doing it like that created a baggy top, which I used to make a ruffled edge when I sewed in the lining (the fabric was a swap extra someone sent me last year). I like the ruffly top. The strap is a crochet chain with the yarn held doubled, then braided. The top pictures are of the bag with Sal (the computer) in it.
I plan on adding some sort of closure... I'm thinking just some velcro at the top. The strap holds well enough for now, but I'll likely change it out for something different soon.