As has been said, probably isn't worth doing. I've tried something similar with a security camera system. The advantage of this was that the system (cameras, IR lights, hard-drive recorder) could be run from 12volts, so no need for an inverter. At night, the highest sustained load was about 150W, average about 100W. I was using wheel chair batteries, which I could get 'cheap' (£50 for a 50Ah 12volt). They're meant to be good for several 100 cycles provided they don't go below 20% capacity and possibly 1000+ if they don't go below 50%. Anyway, the recommendation is that you don't discharge at greater than 0.1C (5A) (otherwise the effective capacity is reduced and keep them at room temperature), so for 150W this means you need 3x50Ah batteries in parallel (or one 150Ah battery) and provided don't run off battery for more than about 10 hours. I had a simple setup, where the batteries were connected in parallel to the security system and there was a 12V charger permanently connected via a timer to the mains. The timer set to be on for 14 hours during the day. Now I have PV, I could have had the charger powered from the inverter (SB4000TL) via the multi-function relay and a contactor to the mains, but likely would have needed another 1 or 2 batteries to cope with winter nights. After about 6 months, the batteries are pretty well shot (now about 60% rated capacity), so just on batteries, I've spent about 82p a night, and could have saved myself about 9p per night in electricity (about 1kWhr at 9p a unit). So even if I could have gotten 1000 cycles (about 3 years) out of the batteries and only charged them from solar, it still would have been cheaper to use the mains.
