Most electric motors have a horsepower rating, but wattage works fine too. You can convert it to horsepower (I like
Online Conversion) However, its kind of a rule of thumb deal. Take your gas engine's horsepower and divide by 4 to get your electric motor horsepower. This is a rule of thumb because a 600W electric motor can put out just as much power as the 1200W motor. It just can't do it indefinitely, at least not without cooling (assuming brushes don't blow or something else). The 1200W motor will be able to sustain twice the power of a 600W motor without overheating or causing damage to the brushes or commutator.
I can tell you, with my ecorider mower, I'm using a 24 volt 1.6hp motor. This weekend I hooked it all up and drove it around and I was drawing 100 amps fully load @ 36 volts. This translates to 3600W, or 4.8 horsepower. Now, my motor is fairly large and didn't even really warm up for the short periods that I ran it around the yard. So, weight also has something to do with it. This is kind of why most guys measure their motors in diameter. Mine is about 7" in diameter. I'd also imagine a motor like mine being plenty for a go kart, especially if you have multiple gears. In third gear that thing got moving.
Of course, there is always a simple single geared setup like Ben's motorcycle too. That thing goes plenty fast too since its geared correctly. It still has plenty of torque too!
Have fun with the project! If you make it up here for an EV build day we might even be able to get you some parts. I know I have extra contactors.