I've always played the game with a joystick. Last joystick I used for this game was a Logitech Extreme 3D Pro, which worked fine. The hat I used for switching Primary/Secondary Weapons as well as couple of shield controls. For the side buttons, afterburner was set on one. Don't remember the other settings.

Not sure if it's possible to fly in this game with a mouse, if so, it would be quite difficult from what I remember from X-Wing days.

I used a combination of keyboard and mouse. It's great and much easier than on the keyboard itself. It resembles an FPS game a little. Joystick is probably the best choice however.

Joystick (a Saitek ST200 USB I bought together with the first Freespace) and keyboard for most of my life and since a few years ago a joystick+throttle set (CH Combatstick and Pro Throttle).
I did try once with a mouse, it's probably doable but not my cup of tea as a control system for a flight game.

I've always played the stock games with a joystick but beware that there are some mods out there like that Wing Commander mod that is unplayeble with anything but mouse and keyboard.

You don't mean Wing Commander Saga, do you? I always played that with a joystick, and also did a run with my current HOTAS setup.

Congratulations for your expert skills, I couldn't hit those damn flies or hornets what they're called in the first few levels, things only improved when I switched to mouse+keyboard but I didn't play much beyond that.

IIRC I played at a lower difficulty level (either easy or medium) as the developers recommended.