Best Fighter

[the phantom]

Boromir, Eomer, and Gimli

What? You're leaving out Faramir? From ROTK, The Steward and the King-

...and yet knew, for she was bred among men of war, that here was one whom no Rider of the Mark would outmatch in battle.

I would pick Faramir over Eomer and Gimli.

Boro88 has nominated Hurin for best man warrior. He may be right, but I would choose his son, Turin, over him.

And Fea is right to mention Denethor. He is worthy of some recognition. From LOTR, Appendix A-

Denethor II was a proud man, tall, valiant, and more kingly than any man that had appeared in Gondor for many lives of men; and he was wise also, and far-sighted, and learned in lore. Indeed he was as like to Thorongil (Aragorn) as to one of nearest kin...