Nothing helps functioning in low-light situations, like overcast and cloudy days, better than excess panel area.
I have a minimally-sized panel I use for powering a laptop and it's rather annoying to have it underpowered in the slightest deviation from ideal circumstances. That same panel for charging smaller devices over USB like phones and tablets is an absolute dream thanks to the overkill, even overcast and cloudy days it never quits charging.
My laptop accepts the 18VDC input directly. It works fine when the sun is high and sky is clear, as long as I'm not doing anything particularly CPU/GPU heavy.
It would be nice to log the power consumption and the battery voltage but I didn't do it for this project.
Since the solarpanel is more than half of the budget, I would think, you can actually buy a cookie for ordering a cheaper one.
I think it depends where you live and if the setup should also run in the winter.