This is a collection of illustrations that things are more complex than can be revealed in a one-page intro. Again, drill down for more info.
Solar panel output will almost never be as high as the claimed output. In fact it will probably hover around 75% of that number under the best conditions; this is called “derating”, or correcting output to actual conditions. It sounds like fraud but it's not. A panel's power is expressed as a “nominal” rating like 100W as when tested under laboratory conditions. Since the roof of your van is unlikely to meet those same lab conditions, if you think you need 200W of panel you probably need 250W.
Usable battery capacity is about half of nominal capacity. This is due to a quirk of lead-acid chemistry batteries (flooded or AGM). You can go lower than the 50% mark but it generally leads to early (and $$$) battery death. So if you think you need 100Ah of battery capacity you probably need 200Ah.
PWM charge controllers may not be able to get even the derated power out of the panels. This is because the panel makes maximum power for conditions1) at a particular voltage2) which is higher than the voltage PWM controllers can use.3) You can work around this issue by using an MPPT controller, but they typically cost 2-3x as much as PWM.
Charge controllers have specific current limitations. Regarding current they are rated by Amps of output: 10A, 20A, 40A, 60A, etc. To protect the controller from damage their nominal output is derated by .80; this assures “headroom” for power spikes due to odd solar conditions. So a 10A controller is safely used at 8A, 20A controller at 16A, etc. If you will be pumping 10A from the panels a 10A controller may not hold up. A 15A or 20A controller may be required. MPPT controllers may be able to cope with excess current.
Controllers also have an input voltage limit which you exceed at your wallet's peril. Going over this limit (usually by wiring too many panels in series) will usually kill the controller and void the warranty immediately. So don't do that.
Vigorously charging a deep-cycled house battery using only solar is $$$. But it takes a much smaller and cheaper setup to charge in combination with alternator, shore power, or generator.
12v systems are not really 12v. We call them 12v 4) but deep cycle batteries are over-discharged at 12.0V; they should probably never go lower than 12.2V. During some stages of smart charging they might be over 15v. It is very common to hold well over 14v for hours during the Absorption statge.
Shade will clobber your panel output. Even a tiny amount of shade will usually have a drastic effect, losing up to 90% of what you might otherwise harvest. This means no tree shade, no antenna shade, no roof vent shade, no roof rack shade, etc.
Flooded lead-acid (FLA) batteries need to be “watered”. They lose water as part of their normal charging and need to be checked and replenished with distilled water regularly.
AGM lead-acid batteries are not well suited to solar-only charging. They cost about 2x that of FLA, have less capacity, require vigourous charging and cannot be charged as high in voltage. They remain popular because people think “$$$ is better” and are loathe to vent their banks.
It is possible (though uncommon) to have one all-purpose battery for both house and starting. This only works when daily power requirements are quite low5) or when opportunity loads are agressively utilized. There are two approaches to such a setup: