D&D 5E - Best Kensei weapons?

Kensei is an interesting class. While I generally consider it a trap option, I haven't given up on it quite yet. The obvious problems with the class are twofold. 1: the class naturally gets the sama damage at higher levels making the choice of weapon pointless after 11. 2: the class gets bonuses for not using your weapon at all. as per the 3rd level ability that grants defense when not using the weapon. Iam not pointing these flaws out to discourage you from playing the class, instead I think they are the key factors to consider when determining the weapon you choose.

As Jaelis mentioned above, the whip is an interesting choice. It grants reach which transforms into mobility by allowing you to engage without being threatened by many opponents. Likewise the Longbow is an excellent choice, allowing for range attacks and the use of class features on the same turn.

I think the most interesting interactions will come in the combinations of magic items in your campaign. Weapons with low or no magical + bonuse but powerful secondary effects will be excellent and for this reason alone I highly recommend the long sword as it seems the weapon most compatible with many different enchantments. Abilities like Flametounge, slayer weapons, weapon of warning are good examples of weapons balanced by their lack of +3 variants.

The final and most important consideration is how cool your character will be with your chosen weapon. This is purely subjective but certainly worth considering.

Hope some of that was helpful.