A good regulator/charger is definitely the go, but the most important thing is to properly size your battery according to your load requirements and proposed charge/discharge cycle and then size your panels/regulator/charger to suit (remembering a rule of thumb for solar is roughly 5 hours at maximum panel output per day).
So if you have a load that needs 100Ah/day at 12V then you need a minimum 125Ah AGM battery (based on 80% discharge cycle) and you will need a solar system that will output the 100Ah back into the battery at 14.4V (or thereabouts) in about 5 hours. So this will mean an output of 20A (100Ah divided by 5 hours) at 14.4V which is 288W. This quick calc does not allow for losses and inefficiency, nor does it give you a fudge factor for a cloudy day. But you can easily correct by say doubling the battery/panel size to give two day's capacity between charge cycles and then apply an additional percentage to allow for inefficiency.
A big alternator like the oversized one in my Land Cruiser will pump out over 80A and not care if it's cloudy. In the case above, it will dump 100Ah back into the battery in just over an hour's driving. That's why I reckon if you're someone who is on the move a bit, use an oversized battery and alternator and don't bother with the solar. If you go to a camp for a week and don't drive the car then solar is the go.
I just saw your numbers above surfer62 and I reckon your setup will be fine, you'd probably get away with stopping somewhere for a couple of days as long as you manage the fridge and don't drink too much beer (hot cans will cost you more power to cool down)

Something I should add is that you want some big cable to that battery too (if it's in your tray and not the engine bay) so you don't get a problem with voltage drop when it is charging when you're on the road.