A key is to try to get a handle on why your current batteries failed. Your guess that you cooked them by leaving the trailer plugged in is a good start if you have the typical converter/charger. Low electrolyte levels indicate overcharging that is typical of this situation.
Fix that problem first. If using an old style converter, update to an intellepower with charge wizard or equivalent or use a decent battery maintainer that supports equalization and desulfation.
I am also finding that the old style converters kill batteries over time because they don't charge them properly. You need a 3 stage charger that will get the batteries promptly up to a full charge. Converters kinda' sorta' get there and take a whole lot longer. Vigorous proper charging helps keeps the batteries from sulfating, which is a major cause of death. These kinds of batteries don't do well in float service.
As for batteries, you will probably need group 27 size 12v
RV/Marine duty. Brand isn't so much an issue as is getting fresh batteries from a reputable dealer. For instance, Costco batteries run about $50 and are guaranteed for 3 years and a lot of folks find them a good way to go.
For best battery life, use them so that they discharge to at least 10% but no more than 50%, recharge promptly with a 3 stage charger, and maintain actively with a proper device. You should get 5 years or more out of a set of batteries else something needs fixing in your use, charge, and maintenance practice.
As for some of the issues Lew mentions (plates, golf cart, etc) - those are deeply held and you can find heated discussions about them - I don't think they are worth much concern.