It's playable with KB&M but there's a metric crapton of bindings to remember. Basically, it's 6dof, meaning you want to go for ctrl/space for down/up, probably the usual FPS controls for forward/back/left/right and Q/E for roll. X also is throttle to zero which will be lifesaver. I believe you really want to bind freelook to something, which is MMB by default iirc. That's at least a good starting point, everything else is secondary after these. The only tips I could give you is to also bind the Framshift Drive to another bind from Supercruise, and to bind Night Vision to something because god damn is it useful given that space is black half the time.
All in all, Elite is one of those games where you will spend a good amount of time in the bindings. My first advice would be to get the sensitivity right for flight, and to not use mouse relative mode at the beginning unless you hate yourself. Alternatively, a gamepad probably works well but I have zero experience with this one!
Edit : Oh, also! You start in a protected environment, the pilot's federation or something like that. Do not leave these systems for the time being. You will not be able to return as soon as you jump a rank, which happens very fast. Seriously, make at least a million and enjoy this protracted tutorial, get a Cobra III or a ship you fancy. Once you've touched everything, then you should have a good handle on how to fly in general and be able to get out into the bubble.