So this is just something i build rather quickly actually. Since i like the Rat Covenant, i thought i might adapt a little more to it and added the poison armor parts. Pyromancy Glove doesn't require any stats and it doesn't add any weight, so it's a good choice to keep rolling quickly. Not that a staff would add much, but you get the idea.
This build focuses on strength with it's melee weapons, so the stats you'd want to level are Vigor, Endurance & Strength.
Red Rust Sword, Red Rust Scimitar, Red Rust Shield & Pyromancy Glove.
Armor: Moon Butterfly Hat, Lion Mage Robe, Moon Butterfly Cuffs & Lion Mage Skirt.
Rings: Bracing Knuckle Ring +2, Royal Soldier's Ring +2, Southern Ritual Band +2 & Third Dragon Ring.
Flame Weapon, Fire Tempest, Forbidden Sun, Great Chaos Fireball, Flame Swathe, Great Combustion & Warmth.
Recommended to PvP in Grave of Saints since this is a PvP build and Doors of Pharros requires you to beat Scorpioness Najka, but if you can beat her with some good PvE weapons (or you're good enough) to beat her, then i recommend you to PvP in Doors of Pharros since there are WAY more traps there.