How much battery you need depends on how much energy you consume at night and how much reserve you want. Let's say you just want the batteries to get you thought the night and that's 60% (e.g., solar gets you through the day) then 48 kWh/d x 60% = 28.8 kWh. As 12V, that's 240 Ah. But with a 90% efficient inverter that's =266 Ah.
Most of the math in this thread seemed OK with a cursory check, but Svetz slipped a decimal place with this one.
28,800 Wh / 12V = 2400 Ah.
I agree with the idea of minimal battery, just enough to get through the night.
I make something between 60 kWh and 100 kWh during the day (mostly to bank with net metering) and my AGM battery is 20 kWh, 14 kWh usable. With several inefficient refrigerators/freezers, if I turn off unnecessary yard lights, rope lights, tube amps, it might keep the mechanical timer running long enough to warm up espresso machine by dawn.
You should be able to get through the night with maybe 25% what I've got (cost me $5000). The freezer will do just fine with power off for the night. What, if anything, do you need to power?
During the day, if grid is down, I can run A/C, laundry, anything I want. PV costs as little as 10% what batteries do, so I'd rather waste photons than waste my money on jugs of deteriorating chemicals.
I don't think you've said why you want batteries. Net metering or zero export can be done without batteries. Some inverters are batteries optional, so you can put in a small battery if you want, or not.
AGM like I use is a reasonable choice for backup, at most a few hundred cycles in 10 years. If you want more cycles LiFePO4 will do it, but most will cost as much as utility rates so no savings. Only lower cost batteries made from recycled cells, or DIY batteries, offer savings per kWh. DIY LiFePO4 can be lower up-front cost than AGM, so worth considering.
Right now everything is hard to come by. Some lead-acid batteries have 26 week lead time.
PV panels lightly used are a good option. I would select best brands and more watts per square meter rather than cheapest per watt.
store.santansolar.com