SOC = state of charge, but I think you figured that out. Anyway, 100 means 100 total, and you should not think you will get to use all that on a regular basis. Conventional "wisdom" says for AGM deep cycle, don't go below 50%...50 ah in this case. (Starter-type batteries can't withstand repeated deep discharge, even to 50%, so you would get even less if repeated daily). Also in real life, you can't assume you'll be at 100% every evening when you start drawing down. I'm not sure what's under your driver seat, but I have the low-end non-AGM single factory battery...which is acceptable if using it only for starting the van. My "house" battery is AGM. If you can afford lithium or lithium PO batteries, my advise is not relevant. But you can waste your whole life trying to have the perfect solar, so don't overthink it like I'm prone to do.
Ok last bit of overthinking: if you don't already have a charge controller, here's my feeble attempt to help. Bigger = more expensive. Higher quality = more expensive. MPPT = more expensive. If you keep you panel small, a 10 amp could get you by, 15 possibly better, 20 overkill (for 125watt solar, but see below). Bigger panel would move those numbers upward. I can't remember Orton's controller, but he could probably max out a 30 amp controller with his panel. MPPT (vs PWM style) will squeeze a couple extra amps out at best (for my-sized panel) but that could be crucial. Most panels are 18 volt or higher. The higher the voltage, the more difference a good MPPT will make. A super-cheap MPPT may make no difference, and possibly be worse than a comparably-priced PWM. I have good quality Morningstar PWM with a voltage, load, charge current display. It taught me a lot to have the display. Not to be a shill for CTEK, but I kinda wish I had bought their d250s instead of the Morningstar, because theoretically, it would eak out a couple extra amps from my panel, but more importantly, it should be able to easily attach to the alternator and provide non-solar charging while you drive (or anytime motor is running). But no display, so less visibility into what's happening. Red/yellow/green LED's are better than nothing, but I'd miss that display if I change to the CTEK... plus it's expensive. Anyway, last summer, I typically drove back to my campsite each evening, which would have been a great opportunity to give the battery one last charge (from alternator) each evening, before starting the nightly draw-down. And in that scenario, the 20amp rating is not overkill unless battery was already full. Even a 100ah battery could accept that rate of charge. Earlier, I was just saying a solar panel under 200 watt can't provide 20 amps, so the controller would not need to be any larger...if solar-only.
Ok, that's all I know, sorry for the lecture. ( While I was writing and editing and re-editing this, Orton replied with more info)