... I'm wondering would it be more cost efficient to buy a used Robot, or try to learn and build a robot myself?
there are lots of variables to consider like: your current experience on it, knowledge, things missing to learn, budget, and mainly: available time until get it running.
As a reference, In my professional experience, I designed and built an automated robotic plant, based on 6 simoultaneous Kuka style robot arms. It was almost 4 years to get it producing. That's a lot of work. Basically the only I bought was the servo motors and bearings, all the rest was propietary developing. And here comes the point: To develop this it was necessary to:
It comes from high to low level design.
-Whole system concept & dataflow (myself)
-Mechanical (CAD) design (myself) & implementation (external),
-*External mechanical shop
meetings & instructions () (myself)
-Boards design & implementation (external)
-Electric design & implementation (myself),
-Electronic design & implementation (myself),
-Embedded software design & implementation (myself),
-Control software design & implementation (myself),
-Data model communication design & implementation (myself),
-Whole system performance bench & quality tests (myself & help).
-Failproof tests (myself & help).
-Sync tests !!! (myself).
-Security & redundancy tests (myself & help).
-LOts of other tests of lots of other different scopes (myself & help).
... so that's about the things you should handle to develop what you want to.
So that's a quick & fast reference for you to take into consideration to take a desition.
*I don't know in english how they are specifically called, but it's where there are lathes, milling, cnc & stuff and they make the metallic pieces you specify then in mechanical plans like gears, axes, pulleys, structures & stuff.