Also is it possible to completely ditch the UPS and get an inverter+ battery which can also power 2-3 CFL for 10-12k?
Inverter is not good for backup compared to an UPS because there is a gap of triggering the sensor and relay of power in an Inverter where as in an UPS there is instant triggering of sensor and relay of power. So UPS is best for a PC than a Inverter.
A sensor and relay mechanism checks whether the mains is ON or OFF in an inverter. When the mains get switched off, the relay mechanism triggers to switch from mains to inverter. Rest is same like the UPS. Because of this sensor and relay, there is a gap between triggering.
Go with the following according to your budget:
APC 1100VA UPS @ 5300
or
CyberPower 1000VA UPS @ 4000
The above prices are online prices where as they are available for cheaper prices locally like APC @ 5k & CyberPower @ 3.5k