Mik68,
Woodglue points you in the right direction. Since you say you are inexperienced and you mentioned "12v car batteries" I'm going to repeat a significant point. You want deep cycle batteries, not car batteries. They are built to take the charging/discharging much better and will last significantly longer.
So regular car batteries are < 12v deep cycle batteries which are < 6v batteries in ability to take discharge and last longer.
The class of battery (or group such as 24, 27, 29, 32, etc.) refers to how much power they can hold with bigger numbers indicating more power and generally larger size.
As mentioned, charging by driving is going to be very ineffective due to the length of the wire run from the vehicles alternator and the size of the wire. Your choices are going to be buy a genny and feed it gas to recharge every 2-4 days (depending on what size and how many batteries you end up going with and your power usage) or adding enough solar to recover your batteries back up to 90%-95% each day from the usage you had the previous day.
Use the search to read some fantastic posts about both Solar and batteries as both have been covered in much greater detail than I have above, I just wanted to get you some basic info before you went out and bought a couple car batteries that you would have been very disappointed in their performance.