Which gearbox? I know you said it's a '72 but Minis seldom have their original parts. Your gearbox could be a magic wand type, a remote shift, or (most likely) a rod-change box. Take Dave's approach and have an assistant shift it into gears while you look around the car for obvious problems. If the drivetrain problem is in the gearbox, it is difficult to make educated guesses without knowing the gearbox type. As stated above, it could also be missing shafts, linkages that are not engaging, missing primary gear, broken or missing differential gears....
You asked about the costs. As Jerry said, many new parts are available. Keeping a wish list will help you keep track of what the "new" parts will cost. You are likely to find placing a couple of large orders directly with Mini Spares, Mini Sport, Somerford, or DSN Classics in the U.K. will be much less expensive than buying from MM or Seven. Used parts are always an option but people are tending to hoard them a bit these days. eBay can be helpful.
You said rust. Are you planning on fixing the rust yourself? Bodywork costs a lot on any car. While the Mini body is simple it is easy to spend thousands on body repairs if you do not do the work yourself. Likewise, painting a car can be cheap or expensive. If you are on a budget, it is not unreasonable to consider MAACO, Peach, and other discount painters for a driver. If you are going for a concours level restoration... be advised a rebuilt '72 may never be worth the money and time you put into the restoration. Do this as a labor of love, not an investment.