Mission based.
But once you play it you won't care. It's that good.

No, you won't wishlist it. You will buy it right now, and play it. It's beyond amazing. The Freespace games I easily consider to be my best purchases here. And I finished both using only mouse and keyboard without any problems; I actually got so used to it, that when I tried to connect a joystick, I wasn't able to do shit.

For the absolute best experience I'd strongly recommend the Freespace Open engine remake that includes additional graphics settings and such to make the game look even better.
The installer supports Freespace 2 by default, but you will also want to check all the additional options for higher-detail models and effects and whatnot; in order to run Freespace through Freespace Open you need to select its content pack as well. The installer can also set up various mods (I haven't had a chance to try any but they sound really good).
Freespace Open will give you additional executables--it doesn't replace the original ones--so you will need to change your shortcuts to point to the new file. It also has various additional options available through a pre-game launcher.
Yeah, it worked fine. I played the likes of Descent II back in the day with a keyboard only, so maybe that gives me a bit of an edge. ;)
It's a bit annoying at times when enemies are shooting at you from all over because you need to be able to think in three dimensions and read the radar correctly to know which way to turn, but of course that applies to any input system.
Also note that the mouse control is inverted vertically by default--like a joystick--but you can change this in the settings.