I know that game is supposed to be played with joystick, but I don't want to buy it just for one or two games. I enjoyed playing with mouse, but it should be much better with controller. Has anyone found way to calibrate it properly? Despite my best tryes I always end up with cursor sliding around a little bit.

Easiest way is to use program like Keysticks to map the controller for game controls (at least in 1993 version since you can't remap the controls ingame). The problem with xbox controller is the small range of it's sticks: it's impossible to aim properly without making a big deadzone but that makes it impossible to turn as fast as the game would allow (and you will need both precise aiming and fastest possible turning in this game).
I personally used controller with big deadzones and made the speedy u-turns with mouse. Messy but playable. I really recommend getting some cheap joystick though.

edit. and the calibration can be done easiest by emulating mouse with the xbox stick, I never managed to calibrate it properly any other way.