As Benta says, this is a motor that runs at a speed determined by the line frequency. I don't believe it is a synchronous motor where the RPM is exactly locked to the line frequency, rather, it is an induction motor where the RPM is lower and depends on the load. Do you need to vary the RPM?
Here's a description of the general type:
https://www.beckettcorp.com/support/tech-bulletins/an-introduction-to-psc-motors/ You should be able to determine the two windings by their resistance. There is a type of the these called reversible PSC motors where the windings have the same impedance. In this case, it doesn't matter which winding is used as the main.
Do you need to reverse the motor on the fly?
Your run capacitor value is in the right ballpark. Polypropylene is a good choice. I would go for at least a 400 VDC rating.
When it's all done, check the AC current to see that it's not higher than what is shown.