It looks like you have a single pole thermostat so you're wire it as you show in the single pole wiring or thermostat PDF that you posted. You can use NM 10/2 for the wiring, just make sure to wrap the white wire with a piece of black electrical tape at each end to indicate that it is not being used as a grounded conductor, but is now an ungrounded conductor (aka hot/live). I see no reason not to use a 30A double pole breaker over a 20A.