By 12 volt inverter I assume you are talking about a normal 500 VA inverter.
Power consumption during full load charging = 12*15 => 180 watts
Load other than inverter let’s say 1 tv (80 watt), fan(80 watt) and light (20 watt)
=80+80+20=>180 watt
1 H.P motor = 746 Watt
Normal running current = 746/220
Starting current = 5 times =>5*746/220
Starting power = 220*starting current => 220*5*746/220=>5*746=3730 watt
Total starting load = 3730 + 180 + 180 => 4090 Watt
Normal load = 746 + 180+180+746 = 1100 Watt
I would recommend going for 5 KW. You will be having issues later if starting 1 hp
induction motor on 2 KW generator.