Regular brushed motors can be easier to interface to than steppers. If you are using a pic or somesuch, you'd need (input/output wise)
Outputs:
X rail motor drive
X rail motor direction
Y rail motor drive
Y rail motor direction
Z motor drive (winch)
Z motor direction
Claw close (assumes a solenoid)
Inputs:
4 directions
Drop button
Home X
Home Y
Home Z
15 total I/O. A simple basic stamp type BS2 (16 I/O) should work like a champ. Home X,Y,Z can be simple microswitches. Joystick and PB, straight out of any arcade supply place.
Use the motor direction outputs to drive 3 h-bridge circuits (or relays) to handle the motor current.
Programming it should be easier than building it.
You can source the BS2 at:
http://www.parallax.com/detail.asp?product_id=BS2-ICTheres smaller, cheaper pics out there, but for ease-of-learning, the BS2 is pretty good.
The main program loop would look something like this (pseudocode):
Read joystick
Move x&y motors in response to stick
When button pressed
Turn off x&y
activate z for a time period
turn off z
energize solenoid
retract z until home reached
activate x&y until x&y home reached
deenergize solenoid
loop back to start
If you decide to go that route, I can help you with the actual programming if you are not familiar.