1,000 watts is marginal for running a microwave that draws about 12 amps at 120 volts (1,400 watts input for the 1,000 watt rated output power). A microwave will run fine on PSW, but will be damaged on MSW.
I don't know what you plan on running, but a inkjet printer will work fine on MSW, but a laser printer required PSW, or start the generator while printing.
The A/C unit will require 1,500 watts, and will not run on MSW, your battery bank is to small to run it anyway.
A heating device like the coffee maker will run fine on either PSW or MSW, but your battery capacity is to small to run it very long, better keep the 1,000 watt coffee maker on the generator only. That is about a 100 amp load on the battery, or enough to take it from 90% full to only 50% full in about 10 minutes, and it would take 2 hours or more to get the battery back to 90% full with the 120 volt charger.
Personally I would keep the charger that you have, and install a couple of cigarette lighter receptacles. Then you can plug in a 300 watt inverter, small extension cord, and then run all the chargers (laptop, cell phone, ect) that you want, along with the TV, DVD, and such from the smaller inverter.
Have the cigarette lighters installed with #10 wire and a 20 amp fuse. This will allow the lowest voltage drop (due to the large wire) and work fine for the small loads, that a pair of batteries can handle. Then you can take the inverter to where you need the power, plug it in, run it a short time, and unplug it.
I have a 1,500 watt Trace M1512 inverter/charger that I installed in my RV. Normally I let my solar panels charge the batteries, and never turn on my 120 volt charger.
If I am dry camping, and watching TV, my total draw from the battery might be say 7.5 amps with the big inverter running, or only 6.2 amps if I unplug and use my 300 watt portable inverter.
You should consider a couple of solar panels. I would recommend a pair of 140 watt from this place, with aluminum frames, and mount them on the roof, run UV resistant wire (#10 from Home Depot) down the back of the refrigerator vent, to a charge controller, to the battery.
SunElec.comGood luck,
Fred.