Uchigatana is the first katana you’ll find. You can get it by defeating an NPC near Firelink Shrine. The light attack consists of quick vertical slashes, so you won’t be hitting walls and other obstales when you swing. It scales well with dexterity.
Deep Battle Axe
You can get the Deep Battle Axe in the High Wall of Lothric. It is in the tower under the fire-breathing dragon (in a mimic chest). It’s a fairly standard battle axe that does dark damage in addition to physical. It also has a skill that increases damage.
Claymore is one of the first broadswords you’ll find. It’s a heavy, slow weapon with devastating attacks. The light attack is a swipe, while the heavy is a thrust. You’ll find it during your exploration of the High Wall of Lothric. It’s near the Deep Battle Axe, on the terrace the dragon is spewing fire onto.
Partizan is a spear with a bladed head. This allows the user to both poke and make swings. It has a long reach and is great for dealing with groups. You can get it in the Undead Settlement, pretty early on in the game. It’s on a corpse hanging near the cage where Cornyx is trapped.
Irithyll Straight Sword
The Irithyll Straight Sword is a bit special. It has a similar move set to other straight swords, but it’s coated in frost, does ice damage and causes frostbite. You’ll get it from dueling the Outrider Knight in Undead Settlement, the one that blocks the passage to Road of Sacrifice, under the place where you meet Siegward first.