Hi,
I dont have a good program for drawing mechanical stuff either, mainly just electrical. There are some free programs on the web but i never found one i liked enough.
The stepper motor is chosen based on the load it has to drive. It might be difficult to choose one with such an unusual load such as this one though. The stepper motor will have spec's of current and torque, and the torque translates into the linear mechanical motion under the assumed load, but again the load for something like this would be somewhat harder to estimate unless you had experience with that very type of load. You'd have to build up the mechanical part of the machine without the motor and then do some tests with perhaps a spring scale and with the assumed load connected, then order a motor that was oversized to make sure it works. If you only have to build one of these that's not a bad idea, and if you have to build more you could try lower power motors and do some tests.
I dont have any papers on this but you could look on the web i would think there should be plenty of pages that explains torque and how it translates to linear motion. The nice thing about doing it one step at a time is that you dont have to assume too much, you only have to assume that eventually you will get it to work once you have the right motor. You can look up motors to find out what the general size is so you make sure you have enough room to mount it, but that's probably not a huge problem.