I just finished power washing and cleaning them up (what a difference!) and now I want to make sure these bad boys work.
I'm a complete novice when it comes to batteries/electric work. I looked through the forum and am still confused.
The dead batteries that came with the vehicles look like these:

link
I see mentions of getting a 12 v 12 ah battery. I've also seen others use an 18 v (not sure of the ah). How do I determine what the vehicle can handle? Cost aside, isn't it best to get the larger, 18v, battery?
Should I pick up something like this:
ebay link
If so, is it simple to separate the plug back that the Jeep currently has installed and wire directly to the battery? Is that even the correct procedure?
I'm happy to tinker but would hate for my daughter to be driving around and then the car sets on fire :-x