Find an old/used/refurb treadmill motor. They usually come in 2 flavors, 12vdc and 120vdc. You can find these for 25$ with a little effort. For your throttle, you can use a PWM with IGBTs & heavy duty inductor for the 12v motor, if you are using a higher DC voltage source, say above 60v, use the 120v motor and a Mosfet switching circuit. Careful about rating HP. Electric motors fed to the wheels is not like a gaz motor, you will get really fast really quick, even feeding 60v into a 120v motor. Unless you are very heavy, feeding 12v into a 12v treadmill motor may peel rubber if geared accordingly. You will want high current wiring as well not to loose power, we are talking in the neighborhood of 4 gauge wiring with huge lugs at all the connections. This is the advantage of high voltage, you wiring thickness goes down, but if you are using an inverter, you will want even thicker wiring between the battery and inverter, like 2 gauge since this is where all your losses will be. This is the el-cheapo method.
Your other solution is getting a BLDC hub bicycle/scooter motor. These motors are the wheel and use neodymium superconducting magnets, brushless 3 phase. They are as efficient as you will get. There are many controllers for these designed to run off of Lipo battery packs at 48v & 72v and they have built in throttle, battery charge display & regenerative braking. Many are available on Alibaba & you can hit speeds over 30mph with even the 48v ones. However, expect to dish out in the neighborhood of 500$ for a semi decent unit not including the batteries.
For the DC 12 treadmill motor, you can use a 555 to pwm it, but, I would recommend a MCU so with your throttle control, you can limit current, limit acceleration, limit overheating of IGBT and monitor battery voltage as well as some other simple useful functions.
A good treadmill motor should be rated at least at 2hp continuous. I know my 120v treadmill motor is rated at 2.5hp continuous, and was designed to be driven with a square wave PWM as stated on the motor.
For a cheaper 1hp treadmill motor, if your go-cart is designed well, it will achieve 30mph. (For this guy, you can use 8 gauge cabling and still get good response. This will operate max in the 1kw range)