Axes- Use the Bandit Axe if you just want to win, although the Dragonslayer's Crescent Axe is just so sexy looking.
Bows- Dragonrider Bow all the way.
Claws- Manakin Claws are the best, but none of the claws are particularly good (IMO)
Crossbows- I actually use the Light Crossbow the most. It's light enough to stick in an offhand slot and forget about.
Curved Swords- Warped Sword if you just want to win, but I've always preferred the look of the Red Rust Scimitar's moveset.
Curved Greatswords- Murakumo all the way!
Daggers- The Thief Dagger is fun and effective, especially at low SM. Although the Royal Dirk just got a buff to its counter damage, so I look forward to giving that another shot.
Fists- Bone Fist + Caestus powerstance.
Greataxes- Crescent Greataxe! Really, it's more of an axe/halberd hybrid. One of my personal favorites, and often overlooked.
Greatbows- Alonne Greatbow looks the coolest IMO.
Great Hammers- Malformed Skull, especially at low(ish) soul memory, this thing kicks major ass.
Greatswords- All of them are fantastic, but I always come back to my Claymore.
Halberds- Syan's Halberd 100% Brings back good memories of Dark Souls 1 halberd.
Hammer- Homunculus Mace is pretty good, but it's so ugly I can't really bring myself to use it.
Katanas- Never put any serious time into katanas, so my opinion isn't worth much here.
Lances- Heide Greatlance is sexy as hell.
Reapers- Bone Scythe.
Spears- Partizan has those super-sexy R2s, but shout out to Yorgh's Spear.
Straight Swords- Drakekeeper's Sword because its length is huge help when combined with those 1h R2s.
Thrusting Swords- Estoc is amazing all the time, although Black Scorpion Stinger is unbelievable at low soul memory.
Twinblades- Red Iron will let you win, but Stone Twinblade just got its counter damage buffed, so I can't wait to give it a go.
Ultra Greatswords- Zweihander! Amazing length, great moveset, and hits harder than its AR would have you believe.
Whips- Old Whip.