I am listing some of the things that you need to ensure when you buy an inverter:
1. It is better to buy a 'sine-wave output' inverter than a 'square-wave output' inverter, so that your equipments such as fans last longer.
2. The inverter should have surge protector (guard against voltage spikes) for the charger also, otherwise the batteries would get damaged quickly.
3. The output of the charger should be constant, regardless of the input mains voltage (Better for the batteries).
4. You should be able to select the voltage below which the output should start using battery power.
In my APC home inverter, the output doesn't change to battery power even when the input voltage is below 50 Volts.
This is quiet irritating, as the ceiling fan doen't even turn at this voltage.
5. The invertor sales guy should first come to your house, understand your needs, and educate you on what extra things (such as wires) you need to buy before he comes home with the invertor. My invertor salesman came to my house with the inverter, connected the input to the mains, and said the inverter is working (his job is done!), and demanded payment.
6. The output of the inverter should be connected to the fuse of the circuit for which you need backup power. Ask the salesman to do this for you before you make the payment. It is always better to have a separate wiring to connect the output of the inverter. My (old) house didn't have a separate wiring, so I connected the output of the inverter to 2 fuses that are connected to some lights and fans.
7. The invertor salesman should have a specific gravity meter, and show you the specific gravity of the battery electrolyte (compare this with what is mentioned in the user manual). My salesman said "I don't have the meter, but don't worry sir, the battery is fine". But my battery had spilled almost 2 liters of electrolyte while in transit, and the salesman said "Don't worry sir, I will fill distilled water to top up".
Remember the warranty in most cases expires in 2 years, and most defective batteries die just after the warranty period.
Before you buy, you may need to confirm that these guys really store electrolyte, just incase you need it. During each service, they should check the specific gravity and add electrolyte/distilled water if necessary.
8. The salesman should show you the voltage of the battery and the voltage output of the charger separately, using a voltmeter.
9. My inverter had 2 years warranty, and the technician was supposed to come every 3 months to top-up the battery with distilled water during this period, free of cost. He never came (saying I never called him), and I also forgot. My batteries went dead just after the warranty period, due to lack of topping up. Remember, it's better for their sales if your battery dies early. Get these things clarified when you buy the inverter (It doesn't hurt to get in writing that filling distilled water every 3 months is their job without your reminders.) Best thing is to add distilled water yourself periodically.
10. The most irritating part about my service was that the guys who were very polite during sales ("Sir, I can come even on a Sunday") started turning arrogant for Service ("I can come for service only during office hours from Monday to Friday, so if you need to take leave for this, it's your problem"). This means that you need to research on the service BEFORE you buy.
11. If you want your batteries to last long, connect only the minimum load, and don't drain the battery too much. To give you an idea, Inverter Batteries that regulary drain only less than 10% are known to last even 15 years, provided you top up regularly with distilled water. Inverter Batteries that drain more than 50% are known to last less than 3 years.
Also remember that higher connected load means 'heavier' batteries that are costlier (My inverter is supposed to support 5 fans, 5 lights and a TV for 2 hours, and I need two 80AH batteries worth 15000 Rs. Now I feel I should have opted for half the load, and I could have saved half the price each time I buy new batteries.)
12. It is better to buy both the inverter and the battery from the same person (at least during Warranty). If your battery dies, to deny you warranty, the Inverter vendor may claim that the battery is defective and the Battery Vendor may claim that the Inverter is defective.
PS: Do you really need your A/C and Fridge running on the Inverter? Then the required inverter/battery capacity would be huge.