Zolly

I've got one of those wattage meters on the way from Geewiz. Will run some tests over a few days to see what peak and average consumption is.

The hardest part here is getting an accurate measurement for power consumption of your PC. While gaming my rig uses between 250-400W. Assuming worst case of 400W x 3 hours = 1200wh of energy.
Those Mecer inverters are good bang for buck and my first suggestion to people in your situation. You've then just got to work out if the batteries are enough storage. Being lead-acid batteries, you don't want to discharge more than 50% max in order to get decent life from the batteries.
12V x 100ah x 50% x 2 batteries = 1200wh - exactly your requirement. So you should be fine with this arrangement, although it is cutting it fine... Basically you're paying for it with less overall cycles from the batteries if you consume more than 400W.

You can go for an inverter as you have indicated but these are not very efficient. (i.e. Using a low voltage battery to generate 220V only for that voltage to be reduced to the battery voltage again)
What you could try is to use a power supply for your PC like this: https://www.powerstream.com/dc-pc-48v-1200w.htm
So with only a battery bank (don't use 12V!) of 24/48V you could keep your PC going for longer by comparison. You will also need a charger..
I don't know if your monitors have external power adapters but if so you can power them directly from 12V (which is their typical supply voltage)