I am trying to get solar installed, but it is my understanding that if our panel bus rating is 100A or lower, we'll be limited to the size of the system we can have installed. But if it's 125A or higher, then we have a lot more options.
If your panel is 100A bus rating, then your solar is limited to 20 amps.
If 125A bus rating, then you're "limited" to 50A solar.
You've included one picture and all you're going to get out of that is a panel review :) To get more info, you'll need to show us a photo of the panel's labeling, a large sticker with dozens of types of info. It is commonly on the door, or on the interior side of the deadfront (which is the screw-down panel you here removed).
The panel labeling will also tell us the manufacturer, and thus, which breakers are permitted in the panel. Incorrect breakers run the risk of series arcing on the incompatible bus stab... Fortunately the AFCI detects that, so I'd call that one a low priority for replacement. Just don't buy any more of the wrong AFCIs or GFCIs... they're expensive!