What equipment do I need?

In general, the answer is pretty simple.

An inverter, some batteries, and some kind of transfer switch.

The specifics get very complicated quickly.

The first step in my opinion is to perform a power audit. Figure out what you want to provide backup power to (specific items like a fridge, freezer, heater etc., or whole house) and then figure out how much power they take and how long you want them to be able to run when power goes out.

Once that is done most resellers can help you calculate a system.

Just a couple of things I would recommend, if you even think you may want solar at some point, then get an inverter with solar charge controllers.  slightly oversize your system. And make sure you can expand it if (when) needed, you will want to expand at some point and an expansion vs a replacement is much less expensive.

Also, if your area does allow to sell back to grid and you might get solar, you may seriously think about getting a Hybrid system instead of an off-grid system.  The naming can be confusing but in general terms - Off-grid = no sell back to grid but most still allow for grid to charge and bypass system, Hybrid = sell back to grid capable, not necessary but capable.

Good luck and keep us posted,

JB