Welcome to the site.
Might I suggest sourcing a GY6 150cc engine? It will have the engine and trans all in one.
If you were to mount an engine with direct drive to the axle, you're going to have a ton of problems. First one being the second the engine is started, the buggy will begin to move. You need some sort of centrifugal clutch between the engine and axle.
Another problem would be gearing. That's where the Constant Variable Transmission (CVT for short) comes in great. It gives low end TQ, and varies automatically to gear up for higher speed.
You can use that engine you have, but will need something like the Comet CVT to make it work.
On my nephew's kart, they use a jackshaft to get the drive chain where it needs to be.
Long story short, look for the GY6 engine as I suggested before. MUCH easier.
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