I don't use batteries for busking, but I can provide some advice about using them in general.
Tripp Lite sells inverters, e.g. the Tripp Lite PV1000HF.
For batteries powering a ~500W load for any period of time, you'd be looking at some deep cycle batteries, to be able to supply the amount of Amp-hours necessary. I would not use car ("starter") batteries, or even marine batteries. These batteries are designed to supply high starting currents but are not built for capacity.
The cheapest source of Amp-hours I've found are 6V Golf Cart batteries. You can buy them at Costco. Two of them in series will supply about 170 usable Amp-hours at 12 V, which gives you about 2kWh of energy. 1.6kWh of delivered 120VAC if you figure that the inverter is probably about 80% efficient and account for its overhead, which would run your 500W of draw for about 3 hours. It may even be less depending on the discharge curve of the battery for a 3 hr. discharge (effective battery capacity goes down for faster discharges, the provided rating might be for 20 hr.).
The batteries weigh about 80 lbs. each, so 160 lbs. of battery will get you three hours of runtime. Add more 12V pairs in parallel for more Ah / runtime. If you want anything lighter you'd probably have to look at a small inverter generator, and you would have to be louder than said generator while playing.
For charging flooded lead acid batteries I find the Mean Well switching chargers do a good job at a reasonable price, e.g. the Mean Well PB-360P-12 (can be found on electronics suppliers like Jameco -- sorry, I can't post links yet).
Use thick cables for charging, discharging, and linking your batteries. At least #6 to #8 AWG for your stated 500W load.
