I fully support your intention to learn in a practical environment rather than only listening to theoretical sessions at your school. Thus you know what you are talking about …
Another question would be: what is your budget limit?
You are talking about getting some stuff from your father; but there are still some investment (besides of time - don’t underestimate, this will be your most time consuming project ever so far) questions to decide.
I’d like it to be as big as a smaller desktop, at least.
So it will be in the range of, let’s say, 400 x 600 mm (outer measures), which will result into something like 300 x 400 (X x Y) mm working space.
If your budget allows, go for aluminum extrusions (pre-cut with very little tolerance).
As @MarkT said, take the ball screws rather than belt drives as you will need the force to cut (wood, aluminum, steel ??). I built a small CNC made of extrusions - but primarily I am cutting wood (soft- and hard wood, acrylic and sometimes thin aluminum). My machine has trapezoidal spindles, which for my needs is sufficient.
Currently I am busy with a new project, a very small laser engraving machine, which came as DIY kit, made of aluminum bars, driven by belts - as there is very little force/torque needed to move the lightweight laser around.
That said: if you are to cut something, I would go with the ball screws rather than belts, which might work, but a ball screw is the better choice. But you also have to consider, what kind of linear rails you want to use.
They start with simple tray sliders (I am kidding), bushings/rods and go to very expensive linear motion systems. Have a look here.
This site is a wealthy source for CNC newbies and experts as it covers most of the essentials for CNC’ing. You will find a lot of answers to your questions here with a systematic approach as it leads the builder through all steps and decisions.
Having decided for the mechanical driving/motion system you have to decide about the cutter (=load on z-axis). Only then we can talk about suitable motors for each axis, the motor drivers and the adequate power supply.
12V is just enough for my tiny laser engraver, but for your CNC we will talk about higher voltage as the discussion goes on.