Even a 800VA Inverter will be more than enough for your need.
I have no UPS. Still can run my PC (having 550W, Dell IN1930 monitor and W8951ND router) for more than 6 hours with a 800VA inverter, when no other load is on the inverter. Be sure to check the battery specification.
I am not sure about which brand/model is suggested. So, let others comment on it.