I am wanting to get a battery backup system for my house at night time. The batteries will be recharged by solar panels during the day.

it depends on the region you want to install your system. check your sun hour, for example 4 or 5 hours per day. since you need 14hours x 4kW = 56 kWh per day.
let’s say 5 hours per day you have sun hour, so your system should store 14kW per hour. if you use 250watts panels, you need 45 panels and an inverter/charger in order to store the produced electricity into your batteries and convert the DC current to AC 110v 60Hz or 230v 50Hz in order to use it for your house.
For this amount of power, a normal car battery (100 Amp hour) you need 47 batteries, it’s better to get higher amp hour batteries. check the battery prices from the link below