Before I begin, let me state that I prefer to over estimate when it is things like this to make sure that I have adequate power.
Based on the 260W listed above, I would recommend at least a 400W inverter. Recommending a pure sine version if it is in the budget. If not get some that is close to pure sine. This will help in making sure that it is as close as to true AC signal as possible, minimizing and damage that the inverter could do to the controller. I personally use a conditioning power strip that I had laying around.
Now to figure out the battery.
1. Convert the Wattage to DC amps. 260W / 12VDC = 21.67A (rounding to 22A)
2. Using the Amp-hour rating for the battery you use (700Ah as an example), divide by the amps that you got from step 1.
700Amp-hour / 22Amps = 31.8 hours ( rounding down to 28 hours to allow for discharge curve based on battery type)
If you want a more exacting idea.....
1. Convert the Wattage to DC amps. 260W / 12VDC = 21.67A (rounding to 22A) and 60W / 12VDC = 5A
2. Divide step 1 answer by 12 to figure out the Amp-Hour for the first 5 mins of startup: 22A / 12 = 1.83Ah
Note: 60min / 12 = 5min (that is needed for startup)
3. Now calculate the Amp hour for the rest of the first hour. 5A * .9167 = 4.5835Ah
Note: the other 55 mins of the hour is 91.67% of the hour
4. All other hours at 5 Amp hours. 5A * 1hr = 5Ah
5. Using the Amp-hour rating for the battery you use (700Ah as an example), subtract the Ah for the first hour ( step 2 + step 3)
700Ah - (1.83 + 4.5835) = 693.5865
6. Divide the number from step 5 by the number from step 4. 693.5865 / 5 = 173.396625 hours
7. I would round down a bit to allow for the discharge curve.
I have similar set up on order for my GMG, but I added a 15W solar charger. I only smoke about once a week to once a month so the Solar would be able to charge the battery on the off days.
A quick google search will find calculators that will give a better answer, but I hope that this gives a good idea.