First question to ask is do you ever use TT when not on shore power. If not then you could go with a small powersport battery ( think motorcycle). This would activate your electric brakes and run 12 volt on trailer for short period. Advantage is weight, dramatically lighter.
If you are boondocking then you will need a deep cycle. Group 24, 27 or 31, bigger is better. Deep cycle is designed for deeper discharge before recharging due to the design of the lead plates and the lead oxide formulation.
AGM (absorbed glass mat) is the latest technology and provides better RC (reserve capacity) but cost more than a flooded battery.
Most batteries are made by East Penn and JCI in the US and they are similar in performance. Trojan, Superior, Crown and a few others also make golf cart and deep cycle for commercial use.
Overall best battery is made by EnerSys sold as DieHard Platinum and Odyssey. Great power and will last a very long time.
Going 6 volt vs. 12 v will extend run time but simply because you are doubling the about of lead. Two 12 volts would give you even more at roughly same weight.
For what it is worth I run a major battery brand in the US so know a little about this stuff.