Do you mean 10 miles each way or 20 miles each way? Makes a big difference. If it's the former, you could easily do it on a slick tired mountain bike. An older rigid steel bike with fender and rack mounts would be excellent, and should meet your budget. If it's the latter, then I'd be looking at cyclocross or touring bikes. Fatter tires are your friend on less than perfect roads. Bringing it in for less than 500 may be tought. Good luck!