There is much timely advice already given. I have been out of the business for a while, much of my knowledge is outdated. In the first place, for the single phase input, the load for the motor will be multiplied times 1.73 for the conversion factor. Then an added 25% for an 80% load on the breaker. If you have (you should) a starter ahead of the main motor, it should have an overload deck as part of the starter. The overload deck will have a thermal device that is matched to the motor. That takes care of the starting load. If you start from a standstill too often, the thermals will trip. A breaker has some thermal time delay, but is not rated for regular control purposes. It degrades each time it is operated.
As noted above, the breaker is sized to the wire. It only protects the wire, not the load. AWG 10 copper is much too small for a 20 HP motor. For even a light load, I would use at least 50 amp wire (AWG 6 copper) and breaker. The actual wire size will depend on how the wire is contained. THHN is a good choice, as it is not only a high temperature wire, but high voltage, oil, and water resistant. As a side note, I have bought Romex wire that had THHN insulation. But that is not universal, it must be checked for each roll. But AWG 6 is the smallest advised. Aluminium wire is acceptable, although I don't like it. But MUST be sized larger for a given protector such as a breaker. An example for smaller sizes is AWG 10 copper for a 30 Amp circuit but AWG 10 Al is only good for a 20 Amp circuit.
Running wire in conduit will have the same temperature rise as does Romex. It must be allowed for if you are running marginal to start with. Romex for larger wire is not readily available, might I suggest type SER insulation. The voltage is not as high (300 V) but is much more common, easier to acquire. SER is what a residence usually has as a service entrance to the meter can. SE if it is mounted in conduit.
Start with the RPC motor. The full load amps (FLA) will be on the motor name plate. Size the breaker and wire based on that number. You can use a slightly smaller breaker and wire because the motor is starting unloaded. It is not recommended but is an area that can be marginalized. So long as the breaker matches the wire size. Multiply the FLA times 1.73 to compensate for single to three phase conversion. As noted above. Then add 25% more for keeping the breaker from running at full load. NEC says 80%, it may be higher, but is not "code".
Next is a starter. The overloads have a number that determines the current rating. The included OLs may or may not match the motor FLA. Size them as needed. Every manufacturer has a different system, but they all work basically the same way. The starter may be operated with simple (3 wire) or complex controls. The control circuit is up to you.
On the output of the RPC, a three phase panel is highly recommended if there is more than one load. For a single load, a disconnect is enough. Fuseable is recommended. Like before, the wire size must match the overcurrent device protecting it. The usual size for a fusable disconnect is 30 amps. That means AWG 10 wire. . . There are smaller disconnects for single phase, but I've never seen one rated 3 phase less than 30 Amps.
EDIT:
In the old days ('70s pre OSHA) we set up a row of disconnects to feed multiple loads rather than using a distribution panel. The proviso here is that the feed to the 'top' of each switch was the full sized wire used as the output from the RPC. Such a setup would have a 'gutter' for the incoming line with each switch fed parallel from there. It likely is no longer a 'to code' installation, but is safe enough if properly done.
End Edit
Electrical systems are a complex subject. The information given is a basic overview. There are many details not given, they are a matter of your own discretion. Details such as wire size and type, conduit types, and the like. The details given are the minimums. The NEC requires much studying, and even knowing the language before study. A professional installation is not required, but is highly recommended, if only for insurance purposes. As a note, I speak three languages: English, Electricity, and Computers, And count in 3, Base 8, Base 10, and Base 16.
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Ummm, no. That is a recipe for disaster. #2 copper would be my choice, using THHN.
