PURE
Class: Warrior

Soul level: 125
Vitality: 40
Attunement: -
Endurance: 63
Strength: 27
Dexterity: 40
Resistance: -
Intelligence: -
Faith: -

Weapons: Dragonslayer Spear, Pyromancy Flame*
Spells: Power Within*
Rings: Leo Ring, Havel's Ring

*See the section Notes and customization

FAITH
Class: Cleric

Soul level: 130
Vitality: 40
Attunement: 12
Endurance: 47
Strength: 24
Dexterity: 40
Resistance: -
Intelligence: -
Faith: 30

Weapons: Dragonslayer Spear, Canvas Talisman
Spells: Great Lightning Spear, Lightning Spear
Rings: Havel's Ring, Ring of Favor and Protection

First, I can already hear you say: “W0t iz dis? Spear and NO SHIELD?!11!? Not gud 1/10 would not play!!”
I have two answers for you: 1st, you DON'T need a shield to block attacks that you can dodge (you fast roll on both builds, it's gonna be fine); 2nd, you can get the most out of your spear if you two-hand it, and 3rd, it's good for your health to try out a build that doesn't rely on a shield. You'll get (even) gudder, I promise.
So, no shield.
Both builds are made so that you can roll perfectly with the equipment you've got, there really isn't much room for anything else (the SL130 build can roll with 46 endurance without the talisman, but you need that because of faith, therefore 47).

(for those who don't use save editors and like to be 100% legit)

Your quest in Lordran begins with the retrieval of the Winged Spear, your new best friend until Anor Londo. Firelink Shrine, graveyard, first big tombstone with the big skeleton in front of it.
Go through the first half of the game like you would do normally. Get the Large Ember, upgrade your spear to +10.
Make sure you pick up the Lightning spear in Sen's Fortress, from the first mimic; it's weaker than the Winged Spear upgraded, but it'll come in handy at the right time.
When you reach the Realm of Lords, that's where the fun begins.
You'll have to farm a bit (Gold Serpent ring helps a lot) the Silver Knight spearmen to get your next weapon: the Silver Knight Spear. You will use this for the rest of NG, at least until you meet the requirements to wield your next, and final, weapon. Upgrade the Silver Knight Spear to +5, shouldn't be a problem considered all of the crystal lizards you most likely came across by now, you can also buy Twinkling Titanite from the Giant Blacksmith. At this point, you have a weapon that has good reach and decent damage going for it.
As for the boss, please, please do not forget: you have to defeat ORNSTEIN LAST to claim his soul and for his armor set to become avaiable for purchase from Domnhall of Zena, back in Firelink Shrine.
For the rest of the playthrough, just get the stats you need the most first (faith, endurance, dexterity) and the rest last (strength, vitality).
And when you are ready:

"Show the World that the Truth becomes you."
Give Domnhall of Zena 27000 souls for the armor.
Bring the Soul of Ornstein, the Lightning spear and 10 Demon Titanite to the Giant Blacksmith in Anor Londo. Ask him to downgrade the Lightning spear, this will revert it into its base weapon, then ascend the newly obtained +10 spear with the Soul to create the ultimate weapon. The Dragonslayer Spear.

1) You have THE spear. The longest in the game, second only to the Demon's Spear.
It requires 24 strength and dexterity to be wielded, it has a C scaling in strength, B in dexterity and B in...
...
Why am I even doing this?
I mean, come on, the game has been out for a while, people should at least be aware of this weapon's existence. Oh well, just in case: https://m.youtube.com/watch?v=Cd5EQOygUBs here, have a link to MrIwont4get's showcase/review of the Dragonslayer Spear. It'll give you a pretty good idea of what this weapon is capable of.
That being said, there's one thing that is still worth mentioning: contrary to popular belief, the Dragonslayer Spear DOES work with the Leo Ring. Counter damage, which gains a boost from the ring, applies to all weapons capable of performing thrusting attacks that inflict physical damage. All of this spear's attacks count as thrusting attacks. Granted, this does mean that the lightning part of its damage won't see any increase, but it's mostly physical anyway. In short, if what you wish for is more damage, the Leo Ring would be the way to go.

2) Best strategy: R1 spam all day every day for the win. Just kidding. Yes, you can R1 spam and dish out lots of damage fast, but that's boring (and ineffective: you'll get parried, riposted, wrecked, well-what-is-ited and you'll never want to play this again).
What will take you far is how much you can take advantage of the Spear's moveset.
You thought that the R2s were useless, didn't you? Try free-aiming them. Miss the first one on purpose to invite the opponent with the perspective of a free hit, then turn around during the follow-up to surprise launch them.
You also have a long range attack as the one-handed R2, that can be used to hit people that are running away or while they're trying to gather space for a running attack.
All of this spear's attacks have a time and place.
Protip on how not to get parried... actually, it's hard to parry spears in multiplayer. Now, most people don't realize that and will try to parry you anytime they THINK you're about to attack. What you need to do is simply to vary your attacks, delay them differently each time, switch often between two-hand and one-hand, to mess up their timing. Of course, this isn't foolproof, good/lucky players will still be able to get a parry on you every now and then, but if they insist (try hard, spam), feel free to circle around them for a nice backstab.

3) You ARE Ornstein, the Dragon Slayer, captain of the Four Knights. You have earned your title by destroying the dragons at the dawn of the Age of Fire, and honor it in the present day by hunting drakes. A living legend among Gwyn's knights, the Great Lord put His trust in you by offering you the highest rank in His entire army, as well as a special soul.
You are a leader, an exemplar individual that is held in great consideration by those who follow the will of the Lord, a mighty and feared opponent to those that are foolish enough to oppose the rule of the gods.
Yours is the task of protecting the sacred grounds of Anor Londo from invaders and plunderers. Even as your companions forsook their duty, you remained, bound by your honor.

1) The first would be the armor. Not in terms of defence, since Ornstein's set offers a nice, all-around protection without being too heavy, but because of the 45 total poise you get from it. That's not enough to stand a greatsword's two handed R1 nor any hit from an ultra greatsword/greataxe/greathammer. You'll have to be extra-careful when facing those threats. Learning how to toggle-escape will help you, but otherwise just try and avoid getting hit at all.

2) The second con, though this really only applies to the faith variant, is the weight of the spear. If you rely on both RoFaP and Havel's Ring to fastroll, you'll have a hard time in places that require you to use a specific ring, namely Lost Izalith and the Abyss.
The hardest part, every playthrough, will most likely be the battle against the Four Kings. My advice in this particular situation, especially on NG+2 and beyond, would be to break the RoFaP (you can get two every playthrough) and replace it with the Wolf Ring. You'll still midroll and lose a bit of health and stamina, but you'll have more than enough poise to tank the Kings' attacks and keep hitting them. You're probably never going to see any less than 5 Kings and there will always be one (or many) floating in the distance, because you just don't have the damage output to take down one before the next comes out. Just don't panic (lol, it's a game), stay close to the kings so their attacks only deal a bit of the damage and R1 spam. Heal only in-between kings, if you can.

The faith build will use the Canvas Talisman, since at 30 faith it's the one that offers the highest MagAdjust. Great and regular Lightning Spear are good for bosses and PvE in general, but terrible in PvP. Instead, you can go for Wrath of the Gods or Great Magic Barrier. At 30 faith you are capable of casting most miracles anyway.
To use spells on the pure build you'll have to put on either the Darkmoon Seance ring or the White Seance ring as your second ring, since 8 attunement doesn't grant you any slots. I chose Power Within because I like Power Within. That's it. That's the only reason why it's there. If you don't like it and want something else, you can try Black Flame (pro: you can go by as the boss from the sequel). Also, since you only need Havel's Ring to fast roll, you essentially have a spare ring slot: Leo Ring, Dark Wood Grain ring, Wolf Ring, Red Tearstone ring (when you're low on HP), Cloranthy ring are all very valid options. Leo Ring by default to stay true to the cosplay, but you're free to use whatever appeals to you.

It's been a pleasure.
Feel free to point out any mistakes/suggestions in the comments, as well as your opinions about Ornstein cosplay builds and which would be the best way to represent him.
I truly hope that I at least gave you some ideas. :)

“Now, go. Be proud, be strong, be just. Know your own power and motives, and never let fear overcome you!”