In looking around, I've figured that to power my several servos and one DC motor, I'll need a motor shield, so I can't use a shield to connect the USB joystick to the Arduino board.
Why? Does the motor shield consume every available I/O pin and/or the pins used by the USB Host shield?
So my thought is to connect the Arduino board to my laptop, and the laptop to the joystick. Is there any way to do this?
Yes. Write a program on your PC that reads the Joystick's status and then communicates with the Arduino over Serial.