Mostly down to preference, but I can give you an idea of what each weapon class does. And the 'best' from that class.
-Any non-Artorias/Black Knight Greatsword: All attacks are useable in a PvP setting and are unlikely to be punished by duelers who aren't fishing. Claymore is considered the best.
-Curved Sword: Spam 2HR1 and win. Especially buffed. Falchion is considered the best.
-Spear: Turtle and Poke. As long as you keep your distance and don't get poise stabbed, you'll be fine. Silver Knight Spear is considered the best.
-Straight Sword: Basically a lighter Greatsword. Silver Knight Staight Sword excluded. Balder Side Sword is considered the best.
-Katana: R2 moves aren't particularly good but they have some utility. All other aspects are great. Debate over Chaos Blade or Iato being the best.
-Thrusting Sword: Can turtle, decent all around moveset. Rapier has massive backstab damage. Estoc has good melee damage. Estoc generally considered best for non back stab fishers.
-Ultra Greatsword: Ridiculously hard hitting and has some stunlock. Dead Angles well with practice. Zweihander considered best.
-Great Axe: See above. Black Knight Great Axe considered best.
-Great Club: Ridiculously powerful Rolling R1. Risky to use the rest of the moveset without good spacing. Practice needed. Large Club or Great Club considered best.
-Curved Greatword: Dead angles and infinite stunlock ALL the things! Murakumo considered best.
-Halberd: Powerful with good range, tends to leave you open (if you wiff) for punishment though if your spacing is off. Great Scythe considered the best.
-Dagger: Need to be good at backstabbing and parrying for the most part. Or be willing to wittle away at an enemy. Priscilla's has best melee damage. Dark Silver Tracer has highest back stab damage. Bandit's Knife considered overall best.
-Whip: Trolling only. Guardian Tail with Rotten Pine Resin applied is best.
-Fist: Mostly useless. Claws with Gauntlet of Thorns or Barehanded Dragon Form only.
-Club: R2 is mostly pointless. 2HR1 infinite stun locks. Great STR scaling, slow wind up and short range. Fairly light. Mace is considered the best.
-Axe: Slashing version of clubs, with worse STR scaling. R2 is actually useable. Hand Axe is considered the best.
-Crossbow: Crossbows are useable. Avelyn and Light Crossbow are most popular. Avelyn is considered the best.
-Bow: Actually viable. I believe mostly because you can cancel your attacks at any time. Poison Arrows are wonderful things. Composite Bow is considered the best.
-Great Bow: Trolling weapons. Either of them is completely fine for what they're used for.