Have a seach around this site for inverters etc but just quickly,
I have a 3500 watt inverter, its suitable for motor startup currents and has all the required cut offs, you would need a split charge system and a second battery.
Ive got mine on a converted sack barrow in the back of the van, what this means is that i can unplug the charge wireing and then wheel my mains power to anywhere else the van cant go.
Having a long extension cable is not the way to go with an inverter
I run all my key machines off it (laser, tibbe, mortice+cylinder) and also use it to charge my battery drills and run my transponder equipment, not all at the same time though
You need thick charge cableing and short runs of mains cableing comeing out from it.
There are 2 types of inverter, pure sine wave and modified sine wave, a modified sine wave will clip the tops and bottoms of the ac current form and not be suitable for motors etc (inductive loads) a pure sine wave inverter will output a pure ac current and run anything in the suitable power range.
Modified sine waves are the cheaper ones and pure being quite expensive.
That said ive had a pure sine wave for running stuff on my rally support van and when i came to get another for my lockie van i couldnt find a good one at the time so opted for the modified one as i thought if it blows up ill just by a pure one then, i got it as the seller said it would run a microwave and angle grinder etc, ive had no problems from it but i think if you was to drop below 2500watts you wiull be having problems on a modified sine wave unit.
Hope that helps.