As mentioned, you'll want to match the electrical specs (voltage, phase, amps, frequency should be 60 Hz, etc.) and the mounting dimensions.
Take a photo of the label on the current pump and see if you can order the exact same model number. That's often the easiest way to ensure a good match. The company that makes the wet end of the pump isn't the company that makes the motors, so they may be available from multiple sources.
A local motor repair shop could be an option too. Sounds like it needs new bearings.
Replacing the whole pump would be the simplest route, but the most expensive. If you don't feel comfortable replacing a motor I'd replace the pump, or go with a motor repair shop. The new motor won't come with a power cord so you'll need to add your existing one or a new one.
I worked for Pentair for years, and the pool pumps are basically the same as the aquaculture pumps. The pool ones are just NSF rated for pool use, and the aquaculture models have stainless steel wetted metal parts instead of brass. Other brands that service both industries do the same thing with their pumps.
It's not worth looking at the capacitor IMO. If that's going bad your motor won't start reliably (maybe if you hit it though). Typically you'll hear a "hum" when that happens. If the motor starts fine then I wouldn't go in that direction.