OK here is my take:
a) First you need to determine what you will run and the required capacity. Add all the watts, for motors multiply it by two as they will take that much to start up. That will be the peak load the inverter shall be able to take. The same figure without multiplying the motors by two will be the continuous load required.
b) I would not mix computer or electronic equipment in the same circuit as pump motors, the motors generate a lot of noise and peaks of load that only very good expensive inverters will be able to handle, besides a computer load is relatively small so I would prefer to have then on their own UPS.
c) Now decide the features you would like to have in the inverter.
At least you need switch over, overload protection, temperature protection.
For most inverters modified sine wave or pure sine wave is just marketing mumbo jumbo. All of them convert direct power to square wave using electronic switching circuits and then use capacitors to simulate the up ramp curve and down ramp curb of a sine wave. What I would be looking for is for the inverter to be able to maintain constant voltage for which regulated output is required.
d) Decide how long you want to be able to run.
Battery capacity is rated in Ampere-Hours in other words assuming the Amp-Hour rating is constant at different draws (But it is not, At higher draws the lower the Amp Hr rating) a 100 Am-Hr battery will be able to supply at 12 volts 100 Amperes and will run out in one hour. 50 amperes and run out in two hours, if you want to run for 8 hours that battery shall draw no more than 12 Amperes.
How many batteries?
OK lets start the math.
You have a requirement of 1000 continuous watts so you get a 1200 to 1500 watt inverter (I recommend to oversize it by 20 to 50%) A good inverter will be 85 to 90% efficient (the higher efficiency the less heat it will generate and usually the longer the life) that is if it is supplying 1000 continuous watts it will draw , 1176 watts from the batteries (1000/0.85), rounding up it will require 1200 watts supplied by the batteries.
If the batteries are supplying 12 volts then they require to supply 100 amperes (1200/12) to the inverter.
If you like it to run for 4 hours then you need 400 ampere-hours from the batteries. Because batteries (deep cycle) are designed to be depleted up to 80% of their capacity then you need 500 Amp-Hours, if your batteries are 150 ampere hours then you need around 4 batteries connected in parallel.
The same system will run for 8 hours if your draw is 500 watts.
About batteries types they are designed for the type of work. Start batteries (Like for cars) are designed to provide very high Amperage for some 10 to 15 seconds and then just maintain a small load.
Deep Cycle batteries (Which is what we need here) are batteries designed to be drained and charged repeatedly but can't provide for very large output amperage. They are usually a lot heavier (Thicker Lead Plates) and more expensive.
These are more suitable for power back up or electric cars like golf carts or forklifts.
They range between 100 to 200 bucks each depending on their capacity.
Heavy Duty Industrial type like the ones used in fork lifts can deliver up to around 1000 Amp-Hr each, the price tag could be 3 to 5 grand and can weight up to 1000 pounds!
Marine batteries are basically somewhere in between deep cycle and Start batteries. They are mostly used to run boats and RVs where some motor starting capacity is needed but also can be drained low to run things like on board appliances.
So in summary the cost of the system goes up exponentially with the capacity and length of time you want to run.
If the price is right try a good high capacity inverter. (I think the one linked above
http://cgi.ebay.com/2200-Watt-Power...ryZ85805QQssPageNameZWDVWQQrdZ1QQcmdZViewItem is a good option) even if you run it at only 500 to 750 watts as it has most if not all the features you need including regulated output and aouto switch over system plus charger.
Use deep cycle batteries and try to limit your load to the minimum esentials (Basically the return pump, a heater and some powerheads and get extra 9 V batteries for your controller)
Note that you need to isolate the pump from the main circuit and use the auto switch over system to disconnect the back up from the main and connect it to the pump, other wise the backup will be connected to the main, besides being unable to support the whole system you can put power on the public lines creating a hazzard for the repair workers working outside.
For a pump of 1/4 horse power you need to support a consumption of about 200 watts continuous, 400 watts peak. Add a 100 watt heater and couple of powerheads and an air pump and you are talking for a load of about 400 watts continuous 600 watt peak.
Hope this info helps