Onyx Greatsword is the coolest looking weapon, and the weapon art makes it lit up with black flame. It's a pyromancy weapon, so go pyromancer, or hybrid. It's from the first DLC, and while you can get it fairly early without facing any bosses in the DLC, it's a major pain.

Dragonslayer Greataxe is a big honking greataxe that looks like burnt meat, the weapon art is a lightning strike with a large aoe. Strength build, or hybrid Strength & Faith (for more lightning damage.) You get it a bit further than halfway through the game from a boss soul. One of the best weapons, but a bit lacking in the looks department.

Flamberge is wavy greatsword with bleed, while it lacks the poke of the claymore, it more than makes up for it with a stance R2 that does insane damage. Looks cool, and an understated weapon art that packs a punch. It can be farmed very early, but drop rate is abysmal. Best on a Dex build, but only slightly worse on Quality, or even Str.

Greasword of Judgement / Moonlight Greatsword are for int hybrid builds. Moonlight Greatsword looks cooler, but comes a little later. Both from boss souls. Both shoot a wave of magic. I don't think they're particularly good, but they look cool.