You need an inverter/charger. They incorporate an inverter, a battery charger, and a transfer switch all in one package. Many will also let you add an automatic generator start module if you like. Most manufacturers of these units also make charge controllers. You can program and monitor all the equipment with a common control panel.
Magnum, Outback, and Xantrex (bought out by Schneider, now called Conext) all make excellent units. I've installed them all in various off grid cabins. Magnum is likely the least expensive, Xantrex the easiest to install, and Outback the most trouble free.
