The best battery is the one that lasts long enough. You need to figure out how much battery capacity you need, and for how long. Generally speaking, if you don't run the furnace (the blower motor takes a lot of power) and don't run a TV for hours on end off an inverter you can get away with a single group 31 for a weekend.
While LiFePO4 are the best, they're quite pricey and most people still use lead acid because of the low cost. (I use AGM because I don't like having to add water and like being able to mount them on their side. I also have a > 300 watt solar power system.)
Here's some information that might help:
http://trailertraveler.net/calculate-rv-amp-usage/