Thanks a ton for all this advice, guys. It all actually sounds less scary than I expected. I'll definitely try to get in touch with Valve and just ask how they'd feel about it. I think I might make it even if they don't want it sold, because I think it could be useful to people. But I'd sure not mind making some money off of it, haha! Donations is a cool idea, that might be a good way to go.
I really only had plans for a mobile version, but my prototype is a little C++ Windows program so I could probably do a desktop version if I wanted.