Batteries
In reading your post, it crosses my mind to wonder, do you realize that you Eagle has at least two batteries, and possibly three? There is a battery for the chassis that has a rating in CCA and that is what you want for it. The other barrery or possibly two batteries are deep cycle and are for the coach. When the engine is running they do cross-connect to allow the engine's alternator to charge both batteries (or all three if you have two coach batteries). But when you are parked they are seperated and when on shore power, only the coach batteries will be charged by the converter.
For the coach batteries, I agree with what has been posted, but the very best deep cycle batteries are from Trojan and while they cost more, if you are serious about camping with no shore power, you may find them to be worth the price. If you happen to have two coach batteries, then I suggest that you get two 6A batteries and connect them in series to get the 12V for the coach. I'll not go into the technical aspects of why, but that is only if you have two of them and you may well have only one. I have a friend who has an Eagle but I can't recall if it has two or not. I do know that they really like the coach.
Welcome to the world of RVs!