What size start capacitor should I buy for the refrigerator compressor

Leave the valve closed during storage to prevent moisture, dust, and insects from entering the tank (as @Scivitri wisely mentions in his comment).

Even though any additional moisture could be drained form the tank later, it's more difficult to get the dust and insects out. And they're what's likely to clog up any attachments. They'd also potentially clog the drain valve itself and essentially cause a slow leak until they were removed.

I would return it. It doesn't sound like a lubrication issue - it sounds like either the motor soft starter is bad, is not well paired with the breaker, or is simply not present on that model. AC motors can pull substantially more current on initial start, and I'm guessing that is causing the breaker trips. I don't mean to knock Harbor Freight (much), but higher quality compressors of that size and capacity aren't usually that much more expensive. You can obviously do an exchange and hope for better luck with a replacement unit, but if you are planning on any serious use of it, reliability is a huge plus. Nothing destroys a work plan for the day like having a bunch of air tools that you can't use because the compressor won't start.