Ball screws would be a bad idea. Just use normal threads, maybe acme. Ball screws would have such little friction that loads could actually turn the actuator backwards. Regular threads will give enough ‘stick’ to keep the load where it goes.
My FVC team (FVC-5) from last year had an early design that utilized this very same concept that was put together using only vex kit parts. Ours was basically a lead screw with a threaded beam used as the nut. I will have to post a photo of it later on but for right now, all we did was:
Take a length of square shaft stock and thread one end using an 8-32 die from a tap and die set. We threaded about 10" of the 12" length. You won’t end up with deep threads but step 4 will help overcome that.
Drill an appropriate larger size hole in a pillow block bearing to allow a threaded beam to be forced into it and be held with a good bit of friction. We undersized ours a good bit and used a mallet to force it in.
Drill in a pilot hole in the top of the pillow block to allow a setscrew to ride on one of the flat sides of the threaded beam. We used the long motor mounting screws as the set screw. This was used to additionally secure the beam to insure it did not move when the threaded shaft rotated.
Insert a 1/2" long threaded beam through the hole drilled out in step 2. The 1/2" long threaded beam is a good choice because it is threaded all the way through, and the length and number of threads provides extra bearing surface for the shaft threads to push against without striping out.
Now we had a threaded shaft that could drive a pillow block mount. Thereby converting rotating to linear movement. It was pretty slow moving though. With 32tpi and a 100 rpm vex motor bumped up to 300 rpm through gears, we could only manage 1.5" of movement in 10 seconds. For our application this was just not fast enough, but it worked beautifully.
I know it wont work for competition but I got a piece of 12 inch long threaded shaft the same size and thread as the vex screws. I then went to work with a dremel on one end to square it so a gear would fit. I used one of the + plates from the vex kit and bent 2 sides of it around a nut, putting a short screw and nut on each side to make it captive. It has a little play in it but remains captive. This then can run up and down the shaft and with the 2 wings still straight out it can be attached to things to make a linear actuator.