It may seem a mess to you because the wires are not ordered, coherently colored or labeled, but there is no guarantee that they ever were. Perhaps the connectors or other elements appear to be in a poor state, but it is perfectly possible that everything works as intended.
The buttons are most likely start and stop for the motor contractors, in two directions, and maybe the for coolant pump.
If you cannot make sense of it, you will need to probe all connections and draw a diagram, or try to find the original diagagram and most likely y you will understand, of course if you have a modicum if electrical knowledge. If you don't, I recommend that you let someone else work on it.
Personally I do not suggest that you place the car ahead of the horse and start buying niw See first what really goes on when fully using the machine for your purposes. It may happen that you need to spend time and money for something else more urgently.
Besides, even a single phase motor can give excellent performances in conjuction of savvy use of the gearbox.
Learn to use that first.