That’s a complex setup for a first rigging project!
However, I can help - the first thing you can do whilst I get a basic schematic ready for you is to play around with IK constraints. Just do a simple “lever-pulling-on-another-link” type arrangement to start with and get your head around how to set the constraint and the IK properties of the bone - look in the bone’s object panel under Inverse Kinematics (make sure you are not changing the Armature’s IK properties).
A bone will rotate about any or all of it’s X Y and Z axes and will remain stationary, either in the global system or relative to it’s parent unless you change that by moving the bone or it’s parent or the armatures parent, instead of rotating the bone. So there is a bit of homework for you whilst I set up a schematic for you, which may take a couple of days with my current available time this weekend.
Cheers, Clock.
PS. Can I assume you know how to use an picture as a reference image in Blender?