The red jacketed loomex is available in mutliple gages, so it could be 14, 12, 10 etc - you would need to confirm.
As far as the subpanel size, you may be able to get away with 30 amp, but the specs say max overcurrent of 35 amps, so if a 30 amp overcurrent did'nt hold on start up, you may have to consider time delay overcurrent or non time delay overcurrent and be prepared to go up to 35 amps, which means the sub panel would have to be rated accordingly.
