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Always over estimate so use the full rating 12V at 3.0A.
This mean you will need:
3 nights x 10 hours = 30 amp hours.
A 30 amp hour (30AH) battery might last for the three nights. The 30AH rating for sealed lead acid batteries is based on a total of 30AH used in 20 hours. You are using yours in 30 hours so you will get about 32-35 amp hours out of the same battery.
But usually the rule is that you never draw the battery down to lower than 20% remaining power. The most you should draw it down to is 50% remaining in normal use. If the battery goes completely flat a few times then it is stuffed.
So a 40AH sealed lead acid battery would be the best choice.
If you are going to use a car battery, don't put it in the tent because of the fumes (sulfuric acid). Also car batterys are rated differently. Reserve Capacity (RC) is the amount of time it takes to draw the battery down to 10V at a constant drain of 25 amps. Times the RC value by .4167 to convert it to amp hours.
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