Dair and bair are your go-to moves for KOing. Nair is generally stale because you will be using it a lot on-stage, but otherwise nair bair and dair are similar in terms of damage and (therefore) knockback.
Practical advantages for dair and bair in different situations are:
1) Dair puts out a hitbox extended vertically, making it a better option if you need to cover a large vertical area (the most common practical example is jumping offstage to cover somebody's jump, because if you dair above them, you will clip them whether they jump or not, see every axe video ever for examples), whereas bair will extend a wide horizontal hitbox, making it better if you want to cover more horizontal space.
2) Dair is more disjointed, meaning that it is more likely to outright beat moves with their own hitboxes, like firefox or illusion.
3) Bair comes out faster, so it is easier to land on reaction to recoveries like spacie illusion, or the direction mixup of sheik's or falcon's recovery.
4) Bair has more active frames, so if you need to cover a LOT of space while falling, bair can be a better option... this is rarely important though in real situations imo.
As mentioned elsewhere though, your most reliable kill move below is almost always an uair tailspike, either reversed or not. It will send them down the farthest, it comes out very quickly, it is very disjointed, and it ends quickly, allowing you to get back onto the stage or put out another hitbox very quickly if you need to. It's hardest to land, but with huge payoffs, especially against characters like peach, ganon, or samus who are really hard to kill off the side due to weight/recovery.