Your link for the battery only turns up the home page so there is no way to know which battery your considering getting, any deep cycle marine or even a golf cart battery should work.
As far as the home brew generator goes, I used to have one, it worked great, the only reason I parted with it was because it was only a 3000 watt and wouldn't power what I needed it to. If you go to auctions esp farm auctions you should be able to pick up the parts easily, thats the way I did it.
If your building a generator to charge batteries to use a inverter why not just use the generator, I would think you would be farther ahead, you would use just as much gas trying to keep the batteries charged as you would running the generator for short periods of time to keep the frig cold.
So why not set up a solar set up.
_________________________
Shadow out !!!
Prepare Or Not To Prepare That Is The Question. The Answer, You Better !!!