You can get a Trojan 150Ah deep cycle wet cell for $150. Can get from YHI.
Car batteries might be cheap but one deep discharge will kill it.
Bigger battery will take higher charging current, this is my experience so if you just post this way w/o any caution then one fine day someone going get a 300Ah battery connect to their UPS and blow up the recharger circuitry. You can upsize a bit but not too big an upgrade.