Bah. You don't need a joystick at all.
I completed both X-Wing Collectors' CD and TIE Fighter floppy + Enemies of the Empire with mouse and keyboard. It's annoying? Yes. I grew some biceps near the end when you fight so many TIE Advanced foes, and I had to keep my mouse sliding back and forth non-stop all over my table.
However, out of those missions, the mouse gives you the precision to snipe ships at basically max range (1.6 km?) with your lasers. I have been unable to do that with a joystick, ever.
With a joystick i need to move the whole arm all the time while dogfighting, most of my right fingers are basically wasted on just grasping the stick, with a couple of fingers for just shooting and targetting, and for the other functions I need to use my left hand, to control the dials and throttle slider in the joystick. But what is the point? I could just as easily access the keyboard with it!
I have always found the joystick the most imprecise control method. Unless you have a surgeon hand, it becomes impossible to snipe far targets with it without a red lock. Forget about hitting moving TIE Fighters with your lasers at anything farther than 300 meters.
Back in the day, I played this with a friend on his DOS machine and we shared the work: he was doing the "big moves" with the joystick while I would be targeting and sniping with the mouse and controlling the keyboard input like shields orientation and power distribution. X-Wing was a great co-op game!