said by CajunWon: 6' of 14ga wire introduces negligible line loss.
btw: still using this setup which has worked well through a few power outages and many brown-outs.
Some suggestions.
Do not waste time on the little throw away apc models. Get at least SU1000 or SU1400. These go for about $50-100 on ebay. Then get a web management card for the smart slot so that you can easily monitor what the ups is doing.
The battery thresholds are not user programmable, but you can specify external batteries and extend the run time to hours. SU1400 and bigger have internal fans, but for your load it does not really matter.
User bigger AWG wire, 6' is a long piece. Use fine stranded wire that bends easily.
AGM type batteries are sometimes available at reasonable price, a couple of 12V 100Ah AGM batteries would be a lot safer than wet cells.