A decent marine battery is reliable and can carry enough power to run a laptop all day. No need to idle an engine... you can charge it while you're driving. I agree on the generator people. No better way to take the suburbs out to nature.
A marine battery and portable solar panel are not mutually exclusive.
When you've found a sweet spot and have no intention of driving for at least a week, it's less than ideal to repeatedly idle an automobile engine just for charging your battery. Most of the energy is being lost to waste heat, it's a horribly inefficient method and annoying to boot. But sure, charge your batteries off the alternator while you're driving places as well. Everything should get topped up whenever you drive somewhere.
Most state parks I've stayed at around california permit 14-day continuous stays. Enforcement hasn't been especially strict in my experience either unless it's a busy time of year or there's an associated nuisance.
Having access to all the comforts all the time is for the part of your life spent in civilization.
I'd add considering getting a chain gym membership for regular showers.
AllPowers makes an 85W portable folding solar panel that can power a laptop and smartphone directly. I strongly prefer using solar when available instead of having to idle a noisy stinky gas engine at an extended stay site. Some of the most obnoxious campers are the ones who endlessly run generators, don't be that person.