Hi
Indeed if the idea is to really get the most out of the inverter side of that beast, you do need some heavy cabling and a pretty good sized stack of batteries. That's not an uncommon thing to drop in so there are a lot of threads on various approaches.
The most common ways to go:
1) Down to Costco and buy a bunch of the cheapest RV/ marine batteries you can find on sale. Indeed amp hours are amp hours and this does work. You are most likely to haul home a bunch of
12V deep cycle batteries. You are shopping for dollars per amp hour in this case.
2) Get some Trojan T-105 6V golf cart batteries from whomever is cheapest in your area. Since it's a brand name, you don't care who they come from. The guy who fixes golf carts may well be your best bet. They are a well known item with decades of practical experience at using them.
3) (my favorite) Sell the house / take out a loan and get some lithium batteries. Battle Born (and others) will sell you 100 usable amp hours for about $900 delivered. This is getting into the "bleeding edge" of tech so there are risks. You get a lot more amp hours in smaller space / less weight. That makes the install process easier.
When looking at rated amp hours, I would not expect to "use" more than half the rated amp hours on the cheap batteries from Costco. On the T-105's most people seem to be happy pushing it to about 60% of the rated amp hours. With lithium's the number on the label is what you can use.
There are a bunch of fiddly details about each type of battery that need digging into. Lithium happily charges and discharges at higher rates than lead acid. Lead acid capacity goes up if you pull very low currents ( like a couple amps) for a long time. Lithium is not happy charging at below freezing temps.
Lots of fun !!!!
Bob