Similar questions get posted pretty often in engineering subreddits and it's difficult to answer as robotics is so multi-disciplinary.
Very few people in this world are skilled enough in embedded programming, PCB design (motor control and sensors), materials and structures, dynamics and kinematics, controls and machine design (CAD, selecting manufacturing processes, selecting various COTS mechanical parts like actuators and bearings) to be a one-man-robot making orchestra.
Advice to OP: pick a specialization to start with, and focus on learning that while using pre-made parts for the rest. For example, buy a ready-made robotic arm and write path planning and controls software to operate it. Or build your own CNC router/pick-and-place/3D printer/pen plotter but use off the shelf/open-source electronics and firmware.
Once that's done, pick another specialty and move on to that if it interests you.
Picking up this idea, someone should write a robotics version of "Build Your Own Metal Working Shop From Scrap"[0]. It's a seven volume series where basically you start with rocks, make a series of tools, and end up with a metal shop.
Even better if the parts for your robot(s) are machined using the DIY metal-shop tools! It's DIY all the way down...
All joking aside, I've always longed for a complete set of those Gingery books in print format. I have ebooks of most of them, but I'd love to have a bound set. And even more, I'd love to have time (and space) to actually take a stab at building the Gingery metal shop. Seems like it would be real blast (no pun intended).
There's plenty of toy arms for programming on every electronics site, including amazon. They're basically just a series of exposed hobby servos mounted together in a plastic skeleton. The motors are pretty much standard. You can even buy them with or without an control board.
Buy an Arduino Mega or something. That way you'll have way more pins that you'll need, and shouldn't hit up against the memory limits. Arduinos have a huge community, and the free IDE has all libraries and everything you need. I bought one and an MP3 shield from AdaFruit last year and successfully made a GNK droid. complete with flashing lights and multiple modes of tranquil gonks.
Mechatronics, Computer Vision, Control Theory, State Estimation, Path Planning, etc?