Maybe it's just me but I like simple things. Most automotive alternators already have voltage regulators in them, so you should not have to worry about overcharging your batteries IF you select the right alternator. You should also consider a self-exciting alternator because a manually-controlled one will require extra effort (complicated circuitry) to deal with.
To detect end-of-charge, you could use some kind of current sensing device on the alternator output. As the batteries charge up the alternator's output should go down, so just pick a setpoint for the engine cutoff (will require experimentation). DigiKey, for example, lists many "Current Sensing Switch"es so this should be fairly straightforward.
As for auto-start, you can sense low battery voltage with a "voltage sensing switch" -- the second hit in Google for that phrase shows a device that looks perfect for this application.
One thing to consider is that when your fridge runs etc, it will draw the battery voltage down but this does not indicate the true state-of-charge of the battery. For example a fully charged lead-acid battery might read 12.8v with no load and 12.3v under load, so to avoid running your generator unnecessarily, you'll need to have the voltage setpoint lower than you might expect. Or, put another current-sensing switch on the battery output so that you have a better idea of what the battery's state-of-charge is between no-load and loaded conditions.
All that remains then is a starter circuit that is triggered by your low-voltage switch. Make sure that you design it so that the starter will not run for more than a few seconds, to avoid burning up the starter in case the engine does not start right away. If you wish to have multiple start attempts, you'll need a timer or a simple resistor-capacitor combo to delay the restart attempt for 30 seconds or so to allow the starter to cool.
One thing to consider for unattended operation is an oil pressure cutoff switch so the engine doesn't destroy itself should a lubrication failure occur. A over-temperature cutoff switch is another good idea in the event of a cooling system failure.