I suggest starting with the things that will likely cause you trouble and cost you money as they can sometimes be avoided!
Batteries are abig problem on Rv for a couple reasons. One is the way we use and RV compared to what we do with a car. We don't start them and run them long enough to keep the chassis or starting battery charged up! It also doesn't get charged when we are plugged into power like the coach batteries do-----unless we make sure there is something to do that.
Second battery problem is that there are often switches that we think turn off/disconnect the batteries.Trouble being that the switches still leave thing connected that WILL run a battery down if given some time.
Safety equipment like CO and propane detectors are left on the coach batteries. On the start battery, there are often drains like radio presets,igntion or othe small items that can drain that one.
So one way to start out is to try to make sure you don't let the power sneak out of the batteries as that is one sure way to damage or totally ruin even a new battery!
Former owners may not have been up on those points and thought there was not
a problem but it sneaks up on the unaware folks!