If you were not a boondocker, I would say the least expensive deep cycle battery would be fine, because all its really used for is the breakaway cable for the brakes. But since you do boondock, you'll need something more substantial than a cheap battery. We don't boondock anymore, so I'll let someone more knowledgeable answer that.
Yes, it defaults to using the battery. That's because many things in the trailer are 12 volt, the lights, vent fans, heat, and a few other things. There is a power convertor that runs when connected to shore power and converts the AC into 12 volt DC. It knows when you are plugged into shore power or running off the battery.
I have always disconnected my battery when not in use, especially with our new trailer. You can buy inline switches that attach to the outside of the battery box to make it easier.
For tips and suggestions, you'll pick up a lot just by perusing these forums. And don't be afraid to ask questions. Most folks here are very helpful and have a lot of experience.
Chuck D.
“Adventure is just bad planning.” - Roald Amundsen
2013 Jayco X20E Hybrid
2016 Chevy Silverado Crew Cab Z71 LTZ2
2008 GMC Sierra SLE1 Crew Cab Z71 (traded)