Generally the E series will have the same size and offset wheel (and tire) for all positions. Occasionally there are cosmetic differences, such as alloy wheels for the outers on the rear but steel wheels for the inners. I suppose some people may opt to run a different tire on the steer axle than on the drive axle, though that's not especially common.
I would not want to be traveling without a spare and the tools to put it on. My class C came with a spare, which mounts underneath with a cable hoist arrangement. This is quite convenient for carrying if your layout permits as it doesn't take any usable storage space up. Other common setups for carrying a spare are sticking it in a storage compartment somewhere, mounting it to the bumper somehow, or carrying it on a hitch-mount carrier (possibly on the front). Carrying one on a bumper often requires reinforcing the bumper and bumper mounts.
I don't know offhand what portion of class C's come with a spare; some do and some don't and I would guess some have it as an option.
(I was very glad to have a spare a few weeks ago when, on the way home from an extended trip, I had the tread on one of the tires separate and come off. That wasn't a fun situation, but it would have been worse without having the spare!)