Weedie engines don't have the stones to do much of anything except for what they were designed to do...that is...knocking down weeds or grasses.
To expect them to push around 200 or 300 lbs. is a bit much. This is assuming you can manage to keep the pto in one piece.
As far as 2 cycle engines go, I would not use anything below 90 or 95cc's.
A typical weedie engine size is anywhere from 22 to 31cc's (more or less).
A small Briggs 2hp engine is around 109cc's. Not a performance engine, but will move you.
I will only use 2 cycle engines to power my stuff. Lawn-Boy engines (6.5HP @ 141cc's unmodified) rule the day and are plentiful around these parts, but do require work to get them mounted.
As for your question, use a standard mount 4 cycle engine to begin with.
The amount of work it takes to get a weedie engine to do anything is not worth the work and $$$ and will be a disappointment in the end. Fun factor will be close to ZERO.
Others will disagree.