For most new installs the better choice is a DC-coupled battery connected to a hybrid inverter, especially if you're putting in panels and storage together. DC coupling means the solar charges the battery directly without an extra conversion step, which is generally more efficient, and it plays nicely if you later want to oversize your panel array for better winter output.
AC-coupled batteries bolt onto an existing system with their own inverter, so they're often the practical choice when you're adding storage to panels you already have rather than ripping out the inverter. The trade-off is an extra round of AC-to-DC conversion losses. If you're installing fresh and might expand later, a hybrid inverter with a DC battery keeps the most options open.
One scenario worth highlighting: if you want to install batteries now and add panels later (to load-shift on cheap night rate in the meantime), get a hybrid inverter and a DC-capable battery from the start. Make sure whatever battery you choose can fully charge within the cheap-rate window — typically you want it to fill in about three hours during the overnight EV rate.