There is no definite best because it's up to how you like the stats. My favorite is the final boss sword, you unlock it by grabbing it right after you kill his final form.
The fastest weapon is the black mace from the skeletons, you unlock that one by getting a critical hit on a skeleton holding one, or you can just get somebody with it to drop it so you can pick it up.
Chat with our AI personalities
In my opinion, the Spur is the best weapon in Cave Story (some people might like a different weapon better). But, if I'm not mistaken, it does the most damage.