Ted,
There are many choices in RV house batteries today, and probably many more in the future. You decision (choice) will come down to what features you want in the batteries (maintenance requirements, charging efficiency, useable watts, and safety). and how much you are willing to spend. The typical flooded lead/acid golf cart battery is the most bang for the buck, but it has maintenance requirements, is heavy, and has the lowest charging efficiency. The next choice is an AGM (absorbed glass mat) battery. The AGM battery has almost no maintenance, charges more efficiently, and cost about twice as much as the flooded cell battery for about the same life span.
The last choice is a lithium battery in either a lithium ion or lithium iron phosphate (LiFePO4) design. The lithium ion design can be a fire hazard if the battery has any manufacturing flaws like the ones in some of the cell phone and computers in the news lately. However the lithium iron phosphate (LiFePO4) is not a fire hazard, but it has a lower power density. Either of the lithium designs will be 2 to 4 times the cost of the AGM batteries and a properly designed system will have almost no maintenance, and last twice as long under heavy use if the charging and discharging parameters are strictly adhered to.
Gerald