When you say new brakes and gears are you talking about serious hardware like the brake calipers or levers, and the derailleurs, of only normal replacement items like the cables and brake shoes?

It's a big difference, because cables and shoes are fairly cheap whereas if you need more it'll take it out of range.

See if there's a local bike co-op or non-profit repair shop where they can do basic repairs inexpensively, and get a quote for the least you need. Also have them review what else is needed or soon will be like wheel alignment, tires, etc. When you have a handle of the total cost of getting this back on the road, compare that to the BMX bike, or mtn. bike options. Note that you're comparing to a used bike, these often need exactly what you need, cables, brake shoes, tires, and adjustments, so make sure to know the total cost there too.