I would start out with a regular threaded rod. It's cheap and simple to implement. Get used to building a bot and get it into the arena. Then look on ball screws or an acme thread as an upgrade later down the line. Believe me, you will have enough worries getting a robot running in the arena!
For reference, say an M12 threaded rod has a pitch of 1mm. It means that for every one rotation of the rod, the nut will move 1mm along. A 5mm pitch will mean that the nut moves 5mm along for every rotation. But there is a cost, it does mean that the motor will have to work harder to lift the same amount of weight at the end of the arm.
If you do get around to using ball screws then I would recommend covering the rod in an extending metal coil and don't open up the nut, ball screws work in a very interesting way by using small ball bearings to travel along the rod. They are a pain to get back together correctly if you take them to bits.



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