The "trick" to any project is to take it one step at a time. And if you are new to programming, "develop" your program in very-small steps, one or two lines of code at a time, testing before you proceed. This take some practice because the program has to be "complete" and it has to make sense to the compiler... For example, if you chop-off the bottom half of a working program, it won't compile.
You might want to start with the [u]Digital Read Serial Example[/u]. Once you can read a button you can start to "do stuff". ...You could add an if-statement that turns-on an LED or runs the motor while the button is pressed, or make the stepper motor run for 100 steps every time the button is pressed, etc.
The two most important concepts in programming are conditional execution (if-statements, etc.) and loops (doing something over-and-over, usually until some condition is reached).
You can also test the motor separately. For example, write a little test program to run the motor for 100 steps. In a similar way, you can test your motor/solenoid/whatever that's going to cut the wire.
The Digital Read Serial Example, also uses the serial monitor which is one of your BEST debugging/troubleshooting tools. You can send-out little helpful messages like "Button pressed", or "Running motor". The serial monitor can also be sued to "watch" variable values (as with the Analog Read Serial Example).
. Preferably I would like to have a small display/input device where I can set number of cables and lengths, but could accept a computer connected for input if it simplifies things a lot. ..
...Led display with input buttons (or X number of analog buttons corresponding to separate programs)
This can be a bit of a trade-off. If you use a computer you can skip the buttons & display, but you'll have to write a companion computer application as well as an Arduino application. And, writing a computer (or phone) application is another "project".