This proposed system wouldn't work as described. With the quantity of batteries, panels, and your inverter that you've described, the system size would be - 1kW solar, 14.4kWh batteries @48V (see note below), and 1kW inverter.
The biggest and most obvious problem you can't wire a 48V battery bank with six 12V batteries. To make a 48V battery bank with 12V batteries, you need to wire them in sets of 4, so you could have 4 or 8 but not 6. (When you fix this problem, your battery's kWh will change.)
A 60A charge controller would be way overkill. Depending on if you were to go with MPPT or PWM, you would only need between 20A to 30A but there is no harm in going with a larger one in case you want to have room for expansion.
This would make a nice solar system for a camping trailer, or for a remote cabin where the only thing you needed were a few lights. This wouldn't run heaters or a/c but it would have no problem with running the fan on a gas powered trailer furnace. You might be able to run a couple of power tools as well on a good sunny day but that 1kW inverter might be a bit limiting. This is about the size I'm considering installing on top of my work truck but I will go with 2kW inverter so I can run a big compressor in case I ever need to.
The normal way to go about sizing a system is to figure out what you want it to do and then try to size it to meet the need. Both Johnny's and Ⴖuі's comments have good info.