$60 is a small budget.
The only place to go is Hobbyking.
Your old motor runs about 2400kv.
If you change to a 3S (11.1 volts) Lipo Battery your ESC and motor may handle the extra voltage.
My 540 motor and brush ESC handled it OK.
Go Brushless motor Turnigy 2836-3700kv 700watts with a 45A Brushless,3S 2650mah 30C Lipo battery(about the same size and weight as the NiCad battery).
Prop 32mm x 1.4 pitch or start with your own prop.
The brushless motor are very powerful, so 30+ will be no problem.
Connection of brushless motor to ESC.
Centre wire to centre wire and cross over the other two, this will have your forward on the transmitter matching forward on the boat(yes they have three wires not two).