Batteries used in your "house" setup have markedly different needs than the battery that's already under the hood of your car. Not that there aren't similarities, but understanding the differences can help you right-size the batteries for your need and avoid battery murder.
At the very high level, there are lead batteries, and lithium batteries.
While it is possible to use standard automotive batteries that you get at Wal-Mart or the auto parts store as your house batteries, Deep Cycle batteries are better suited to the task. They are designed for more regular/deeper charge and discharge cycles.