If you're willing to spend a little more money, get an AGM type "sealed", maintenance free battery. They will cost about double what a similar size flooded deep cycle will, but they are much more tolerant of high-power pulse draws, which I imagine a travel trailer is well capable of, especially if you have a high-power inverter for running conventional electrical equipment, and you don't have to remember to top them off with distilled water a couple times a year.
You might also look into Lithium Iron Phosphate. They cost about 4-5x what even an AGM will, but they will last 4-5x as long, and you almost can't break them. Note that these are quite different than conventional Lithium Ion like you may be used to from a laptop or cell phone.
As to interconnect with your vehicle so that you can charge it, first make sure your vehicle's alternator is up to the task. You may need to beef it up. And, as was mentioned, make sure that all wiring is done properly. Use sufficiently large wire and make sure all connections are waterproof. This means that connectors need to be purpose-designed for exposed automotive connections, and any splices should be done by soldering the wires and covering with double-wall, glue-filled heat shrink.