If I were buying a battery that is not going to be continually charged like an automobile battery, I would opt for a deep cycle marine or better yet golf cart batteries. But for the application of the FE I don't think golf cart batteries will be practical. They are 6vdc each, hence you'd need 2 and they are about 70 pounds each! However you could get a usable 80+ amp hours from the pair!
Figuring using the FE which is claimed to use a mere 25 watts while running and 300 watts for 4 minute to start. I would even worry about the 4 minute start up for calculating a battery size. P=IE [P=power in watts, I=current in amps, and E=voltage (12.5vdc in this case)] therefore I=P/E, hence I=25/12.5, I=2 amps. So every hour the FE supposedly uses 2 amps or 2 amphere hours, 2AH. A deep cycle battery useful energy is about 1/3 of its total rated AH. So if you need to burn the FE for 24 hours you would need a deep cycle battery rated at 3 times that or 72 AH. That is a very common size battery, probably a group 27, which is the physical size which most cars use. But cars don't need or use a deep cycle battery. Matter of fact if you used almost any deep cycle battery for starting a car you would ruin the battery.
I suggest you get a marine deep cycle battery of about 70 to 100 AH, that is if 24 hours is enough time. If you ever plan to use the battery indoors then a gel cell or glass matt deep cycle battery is best. However, you must make sure the battery charger you plan to use has a gel cell mode. Gels are charged quite differently. They require a lower charge voltage on the high side and higher on the low side! A gel cell does not emit any explosive gasses or for that matter no gasses at all. Do not ever remove the fill caps...if you do you have just ruined the battery! The gell cell battery can be mounted in any configuration however mounting it unside down it will have less than its rated AH.
The best name brand, at a reasonable price, is the Prevailer Dry Fit. Make sure it says Dry Fit. They are made in Germany and are distributed by West Marine. There is a Prevailer (American made)out there but not anywhere as good as the Dry Fit. Exide is a depandable brand for golf cart batteries.
Try Wal-Mart or Sam's they used to carry Exide as well as other marine batteries. Interstate is good but I am not sure if they have deep cycle batteries.
Just don't use a regular car battery...I doubt it'll do what you need in the long haul. They don't like to be deep cycled, they aren't designed for that. The Prevailer Dry Fit is one of the few deep cycle batteries that can be used for starting too. I think the Rolls, and Optima can be also but these are extremely expensive.
I went through this with my sail boat but that needed about 100 AH each day. I used a water generator, the engine altenator, or two 75 watt solar panels. Or a combination of all!
Sorry to be so technical but you asked!
Peter