Hi,
To answer some of your questions, take a look at
http://www.mdspower.com/inverters/inverter_faq.pdf
Remember, square wave inverters could fry your charger unit electronics as well as the batteries you are trying to charge up (depends on batteries used). They can certainly cause the charged batteries in your device to have a reduced life (caused by the harmonics generated by the inverter).
Lots of electronics will not run off a square wave inverter system (ie TVs, Monitors etc).
Pure Sinewave Inverters cost a lot more money (for a good reason). They will run any kit. Just make sure they have a good surge current capability and remember, just because your gadget is rated at say 500W output, this does not mean that is the total power used (could be 750W) It all depending how efficient the device you are powering is.
Rule of thumb would be 1000W inverter to run a gadget / gadgets rated at 750W.

Hope this comment has not caused you more confusion.

Just to give you an idea of new prices in UK pounds:-

For a really good 2000W pure Sine Wave Inverter £1700

2 off 300Ah Gel batteries to connect to it £500 each battery

Then add on cables (70mm Sq) plus battery terminals, relays, fuses etc £150

So you can see how prices go up a lot as the wattage increases.

Conclusion:- Keep it simple. Low wattage if possible (a lot cheaper)

Pay the extra and go for pure sine wave inverter.

regards,

Bob