Try your local bike co-op for a good used hybrid or mountain bike. That would be a great start and shouldn't cost a lot. Personally, I would avoid Walmart bikes, since I've worked on many of them and know how prone they are to failure. Even an old (pretty much indestructible) Schwinn Varsity from the 1970s would serve you better than a new Walmart bike.

I'd make sure this bike could handle a rack.

I'd probably go for wider tires. But if possible avoiding knobbies.