The inverter by itself is a little more involved. You need to know the VA of the motor plus the charge rate/capacity of the cells being used (assuming sealed lead acid).
Battery charging is not an issue. I have a constant voltage charger that's optimized for AGM batteries, and as I mentioned, I have all of the battery power I could ever want. All in, I can easily sustain a constant 4 amp load, continually, for over 12 hours.
So, I have an AGM battery bank, that's charged off the mains with a automatic maintenance charger.
I have a sump pump, its a Zoeller 98-0001 115-Volt 1/2 Horse Power Model M98 Flow-Mate Automatic Cast Iron Single Phase Submersible Sump/Effluent Pump.
It requires 9.4 amps while running,it has a permanent slip capacitor motor. I can not find the VA rating of the motor, I'll assume 1200 or so, given I don't know the reactance.
Based on my math I'd best use a 1,500 watt inverter.
This product seems to meet all of the requirements:
http://www.theinverterstore.com/the-inverter-store-product.php?model=pwric1500w-top-rgb
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