You can usually catch some players off guard by going in with down b. This is good against characters that don't have as much range as say Marth or Samus, who can't react quick enough to deal with it. The reason (in my opinion) this is effective is because of the quick turn around speed that the cyclone has, allowing you to get in and get out if the opponent shields. It's not one of the safest options, but you can see even Abate mixing up his Luigi/Fox matchup with it occasionally on battlefield. I also enjoy using it against an opponent on a platform, as if you hit with it early enough you can fall of the platform into the middle of the stage and put yourself in an advantage if you know you won't be able to confirm a hit afterwards.
There's a lot of talk on pivots as well, and personally I don't believe they offer much reward until the much higher levels of play especially for luigi, but if you can get consistent at pivot jabs or even just pivot shields they're really nice for quick and precise movement options as opposed to just wavedashing.
On the topic of wavedashing, if you can begin to control the distance of your wavedash it will help tremendously. Too many times Luigis will full wavedash in with a downsmash only to get shield grabbed. If you can space properly with wavedash length, you will not only be safe on shield but still maintain your position in the middle of the stage (assuming that's where you are/want to be).
Hope this could help.