Don't use those cheap invertors for charging batteries or you will kill the battery. The only ones that you can safely use to charge batteries is a pure sine wave.
If you want to see what watt invertor you need, just look at the power usage of the item you will be plugging in and add the numbers.
Personally I would not want to use AC voltage that close to water.
Post a link to the lights you are wanting to use. If they are incandescent bulbs you will be ok running 1, maybe 2 with a 400 watt. If they are halogen or florescent 400 will probably not turn them on.