Every NPC you kill comes back neutral in NG+, and your sin is also removed so you'd be doing yourself a major disservice to not do that.

The kellog furysword bores me personally, but thats because im a snob.
My favorite weapons are the
Flamberge
Longsword
Great Lord Greatsword
Winged Spear
Stone Greataxe
and
Demons Greataxe

I'm also growing fond of the ultra greatswords because of this playthrough. I need to see how I like the black knight greatsword and the "greatsword"