RE: Where should the water go...
Get a Dehumidifier running as soon as possible. It will help the drying process a great deal. If you don't have one they can be rented cheaply.
Gary
RE: beginner mess up
Been there too! Sopped up as much with a towel as possible and then rented a Dehumidifier for a day. It was pretty inexpensive and had it bone dry in a day. And, no ill effects. It will pull water from under the walls with a wick effect.
Gary
RE: Buying a new water heater.
I helped my daughter replace the very same model as yours this weekend for the very same reason. She got a new one off Ebay exactly the same as the original. Paid $303.00 with shipping. I think it was over $500.00 from local RV store without installation.
Pretty simple job. Done in about 1 hour including removing the old one. Her new one slipped in the opening without modifications. The wires matched up as did the plumbing. Be sure to check for Gas Leaks when finished BEFORE lighting. I know that seems obvious, but. . . .
She has a switch that lights it remotely with out a gas pilot being lit. I have to believe your original is the same. The instructions show how to wire the switch. We did need to adjust the air control a little bit to get a smooth flame.
Changing manufacturers may mean altering the opening, location of plumbing and etc.
Hope this helps.
Gary