I am wondering how I would create a really simple electronic calculator/computer
Hi and welcome.
Unless you know a lot about basic circuit design and have a lot of experience of circuit building then I would say the project would be unlikely to succeed. If only one in a hundred of your solder joints is dry or connected wrongly, the device will not work and testing it could be a nightmare.
There are many less complicated digital projects that would be fun and instructive to go for first.
Sorry to be a damper but they haven't made 'discrete' processors since the 60's - for good reason.
A calculator/computer doesn't necessarily mean assembling a bunch of logic chips. You could make a simple Electronic Analog Computer which uses electrical components, such as capacitors, inductors, resistors, and operational amplifiers to model physical systems of linear mechanical components.I am wondering how I would create a really simple electronic calculator/computer
You are totally right about the analogue computer and the OP amp in that diagram could be replaced by a very few discrete transistors. That may not be what the OP intended, though; the last time I actually saw an analog computer (explicitly used as such) in use was in the late 60s - just before the advent of Digital Computers for all.
(Actually, the output voltage of this circuit is the negative sum of the inputs...)