Not understanding "battery housing" because I just have a tray under the steps and have to drop the batteries into it. I'm guessing you have some kind of a box, and these come in all different sizes and shapes.
Batteries also come in a lot of different sizes and shapes. For nearly equivalent footprints, some of the most popular 6V deep cycle batteries are somewhat taller than the nearest size automotive battery group sizes. But that is just a generalization. You have to measure your "battery housing" and check that against the sizes of available 6V and 12V batteries. Golf cart batteries get you into a whole new area, because 8V batteries are also common for this application, and you can't make those work for a 12V application.
If they can fit, best bargains in lead-acid batteries are flooded wet cells, whether 6V or 12V packages, from discount markets like Sam's or Costco, because they are decent quality at a good price. Second best, or maybe as good a deal, would be from a golf cart dealer, if they have 6V batteries in a size that fits.
Brand doesn't mean much, there are a lot of brands feeding from a smaller number of manufacturers in North America, or a large number of smaller suppliers offshore. For flooded wet cell batteries, I like Trojan for quality, but tend to buy whatever is convenient locally, knowing I'll be replacing it towards the end of the warranty period.
Best quality lead-acid batteries, whether 6V or 12V, and a lot less troublesome, would be high quality AGM batteries, Lifeline being one of the best suppliers. Sears has been in this market for deep cycle, offering more than one grade/warranty period, but I would go with Lifeline if I wanted to put in AGM batteries.
Lithium is a whole different technology. Weight is way down, energy density way up, charging technology is different, and cost per KWH storage is maybe 10x lead-acid or more. Then you have to find package sizes that fit your need, or change your battery soaces to fit what is available. Lithium technology is lately starting to show up as a factory option (more often a special all-electric model) in the RV market, but it is not just replacing lead-acid with lithium tech batteries, it is replacing the whole electrical system and sometimes the whole mix of RV systems and appliances.