have a look on the back for the input wattage, add 50% to that and thats the size of inverter you'll need. As theres no big motor to start, as in a fridge, you'll not need much more than the quoted wattage of the unit. The best answer to be honest is buy the biggest inverter you can afford (1000-1500w) and fit the biggest cables it will take, with a master switch between it and the batteries. You will use the mains, if it's there, even if for only charging your phone, drill etc. Also for SWMBO's hairdyer, normally 800w.
Even Microwaves have a high starting current. I would test first how much it draws. Testing with the inverter could be expensive. Most are protecting their fuses by blowing expensive innards first (((
Actually I did check, but saw no high start current, maybe an extra amp or two, which is why I said go for a slightly larger inverter. I run mine from an inverter along with a frodge, freezer and a couple of other bits and pieces.
It may be cheaper in the long run to buy a 12v microwave, saw one recently in local caravan shop for under £300, it was a known make (Samsung I think)
If this is any good to you you can call them,
Colins caravans on 0118 971 2424