You are correct about what you need for a 2 and/or three wire pump.
If you have a 3 wire pump, you will need a control box just to run the pump. It will contain the necessary capacitors, relays etc., the motor needs.
A 2 wire pump, on the other hand, will run simply by powering it up.
You could run the pump with just a hose attached, but be careful. Submersible pumps can build tremendous pressures. The hose could be whipping around, ready to leave a welt on the first person it hits.
Pretty crappy, in my opinion, that the owners took all the well controls.
You might consider having the well tested by someone with experience in this. You don't want to buy a house, and then find out the well won't support it.