Building a machine from scratch will be much more expensive than buying one whole in almost every case.

I would say, start by buying a cheaper machine ($1000 or less) that is mostly in working condition and start to take care of, rebuild, and restore this machine until you understand the fundamentals of every working part. I would say best to start with an EM (my opinion).

Alongside that you could learn 3D CAD software like http://www.solidworks.com/ as well as learn a coding language like Python. It is possible for anyone to put all these pieces together to make their own machine from scratch but the first step is to realize the *scope* of what you are dealing with here (and the scope is quite large).

Pinball machines are very complex systems. Manage the complexity by starting small (very small) and working up from there.