My standard answer is 1000 watts. The inverter provides the 120 Vac. The
batteries drive the inverter and the solar/controller recharges the batteries. The size of the battery bank determines how long the inverter will provide the 120 Vac. The size of the
solar panels (100, 200, 300, 500 etc) determines how long it takes to recharge the batteries.
Simple Math:
If you count on 5 hours of full sun 5/24 = .21
If your inverter is 1000 watts and your 12 Volt DC (Vdc) battery is 100 amp hour (AH) you can get 1100 watts (full load) for one hour. 12 Vdc x 100 amps = 1200 watts x .90 efficiency (90%).
If you draw 100 watts continuously from your inverter......you will get about 11 hours.
If your battery is depleted and needs recharge (1100 watts) and you have a 1000 watt solar panel that will provide full charge for 5 hours per day you will get 1000 watts x .21 = 210 watts per day to recharge your batteries.
So conservation and power management is important.
If have more hours of direct sun or a bigger panel (more elements = more power) then the solar recharge watts go up. If you want more inverter run time increase your battery bank (add 3 - 100 amp hour batteries) ...... 4 - 100 amp hour batteries will give you 400 amp hours and about 44 hours of run time at 100 watts inverter load.
I always recommend multiple deep cycle batteries connected in parallel because they deplete much less overall, are easier to fully recharge, and last longer.
Hope this helps.
Cheers!