If you have kids, i would get the 13 or 14.5 (B&S wins over harbor freight). If its an adult toy, i would rather fix up the engine.
You will have plenty of torque (be able to do doughnuts with live axle in dirt) and acceleration and a top speed of 40 mph. I have done two karts with 13 hp engines (converted from 5-6 hp engines). They are fun to drive, and I still feel comfortable letting my kids drive them.
With this particular kart (yerf dog 3203 modified a lot). You may have issued with clearance (eg the engine may run into the back seat or part of the frame). The engine will need a jackshaft/motormount set up. But now that I think of it, you could use that same gas tank and probably clear the seat/frame just fine.
We can help you get the proper gearing and sprockets.
If you want to do the engine/torque converter let us know the tire size, chain size, and sprockets you already have.
There may be some existing jackshaft assemblies I could point you to that go on Manco karts that you can just bolt on rather than making one custom.