I would do the tires as soon as possible. A blow out at speed can be pretty scary and difficult or even impossible to control resulting in more than a trip delay waiting for your ERS to show up. Plus buying a tire on the side of the road can be pretty expensive. If the tread separates it could beat the coach to death and can cause heavy coach damage until you can get to the side of the road.
Dead batteries can more of an inconvenience than a life or death situation as with tires. Dead engine battery you can cross connect with the house batteries or get a jump. If the house batteries die you'll loose the fridge, HVAC, water pump and such unless your converter can pick up the slack. If you have two or more house/chassis batteries replace them all at once. A failing battery in a set could take the new battery with it.
Priorities - Tires (all six), house batteries then engine.