I'm a DK, not too good of one but I know DK pretty well. One thing I can say is you should abuse that tornado without being too obvious about it, because that's your only way to approach DK with any sort of remarkable speed. If they can't space you well, you have an advantage, but most DKs know how their spacing. Some do's and dont's
Do:
Abuse tornado, I hate that move and it's not so easy to intercept. Good to use the moment the DK player gets away from you after a combo, I especially hate being followed by that thing.
Recover HIIIIGH. His bair WOP will kill you very easily.
Abuse fireball, DK doesn't have a projectile. They probably won't damage him but they will keep him busy.
Powershield, you can punish DK with combos if you PS him(unless the attack was spaced very well)
Don't:
It's probably not a good idea to mess with him offstage, chances are you're not gimping him.
Do not be obvious when returning from a ledge, he'll kill you in an instant. Never underestimate that F smash or its range. Better to assume you're in its range and avoid it.
Don't stay on the ground, there's really nothing you can do to him on the ground.
Don't let him reach you.
Don't shield in anticipation of an attack. DK's grab game is deadly and he can also break your shield very quickly.
Basically, he will space you and laugh at your range the whole time, that is until you hit him with a combo. He is also one of the most physically gifted characters. He's faster than you in every way, and he weighs several tons. Don't let him play his game. Don't let him space you. If you have to, just stay completely away until you find a beautiful opening. DK will kill you in 5-8 hits, by the way.
Matchup is 55-45 Luigi IMO.
Stages..DK's best stages are Luigi's Mansion, Brinstar and Jungle Japes. I highly recommend banning Japes. I can't see you winning at all there. Ever. You won't be killing off the top any time soon and unless you land an F smash, you're not going to kill at all. Meanwhile, you die just as early to his punch, F smash, oh and if he grabs you he can kill you at like 30% by stage spiking you into the water. He stands on the middle platform and bounces you off the left one, and if done right you will land in the water and die before you can even jump out. If he grabs you, prepare to tech this.
Though, on Luigi's Mansion you're pretty boned too. Unless one of these two stages is banned, don't expect to beat DK on his CP.
Now, as for yours..Well, don't pick rainbow cruise, for one. Frigate is better. Don't pick corneria either. One grab and he can carry you over to a wall on RC or corneria and execute a grab infinite or a tilt infinite on you that leads into a D smash for an instant kill. I'd say pick frigate just because of that little area on the right. But once you do, stay the hell away from that area because he can gimp you there too. I really don't know what other stage would benefit you, DK is pretty adaptable.
So basically, he will space you and kill you early if you let him, recover very high or be gimped, and tornado is quite nice in this matchup. You can combo him hard too.
Stages:
BAN Japes, avoid Mansion, avoid Brinstar, avoid Norfair, avoid Delfino, avoid Distant Planet
CP Frigate, FD, SV
But I don't consider myself an expert. If another, more knowledgeable DK main contradicts me, take his word for it.