I guess your hub doesn't have the holes for a rotor? If, by an incredibly unlikely chance, it does, I would recommend this Avid's Mechanical BB7 brakes. They are rather cheap (~$40-4$5 with rotor) and unanimously considered the best mechanical disc brakes. An Avid Speed Dial 7 brake lever set would cost you about $20 (seen on Amazon), and it is, likewise, one of the best levers for the price.

You'd be within budget. And your bike would stop when you want it to.