Best for Singles, can work for doubles.
THE GREAT WALL OF SINNOH
Item Attached: Iron Plate
EVs and Nature:
4 HP / 252 SpAtk / 252 Spe Modest/Timid Nature
Defensive build. Cosmic Power buffs both of your defensive stats at once; with base 120 for both, investment in either is optional. Recover instantly heals half your HP, and isn't reliant on weather (like Moonlight on Clefable). I should point out that Arceus is one of a select few Pokemon that can run that combo, the others being Starmie and Deoxys. Judgment is your primary offensive move, and stops you from being Taunt-bait. Final move is up to personal preference, broken down based on what you need most on your team. Do note that this moveslot determines your checks and counters to a large extent.
~Status: Will-O-Wisp (shuts down most physical attackers and makes you near-impossible to KO by physical attacks), Thunder Wave (stops most sweepers, especially Ho-oh).
~Support: Gravity (not widely available, and the others who do get it usually have better options available; ONLY USE IN DOUBLES), Roar (force out counters, make sure team has a Hazard setter for best effect), Light Screen (make you near-impenetrable on the Special side and protects teammates if you need to switch), Reflect (same as Light Screen but for Physical), Safeguard (immune to status), Stealth Rock (you are bulky enough to set your own hazards), Snarl (same as Light Screen, but deals damage), Substitute (makes you near-immune to damage after a few boosts of Cosmic Power), Defog (removing enemy hazards is always appreciated).
~Coverage: Seismic Toss (Blissy, Calm Mind-users), Earth Power (Dialga), Ice Beam (Groudon, Rayquaza, Lugia, Garchomp), Giga Drain/Energy Ball/Grass Knot (Kyogre, Groudon), Thunder/bolt (Lugia, Ho-oh, Kyogre; I personally don't recommend Thunder outside of rain even with the difference in power from Thunderbolt), Shadow Ball (Giratina, Mewtwo, Lugia), Flamethrower (more useful once Ferrothorn, Zacian, etc are legal, but stops Bronzong and Magnezone), Dragon Pulse (Rayquaza, Palkia, Giratina, also has good coverage with Steel), Dark Pulse (Giratina, Mewtwo, Lugia), Psychic (more useful once Eternatus is legal), Surf (Groudon, Ho-oh), Charge Beam (offense with a good chance at increasing SpAtk). As of this post, I understand that Arceus isn't legal to fight against anything released after Gen IV, thus why Pokemon such as Zacian and Reshiram aren't getting much attention here.
EV's and Nature are to maximize Speed and SpAtk. Odd priority for a wall, but Arceus' base stats allow it to outrun most other Ubers and deal far more damage than other "wall"-inclined Pokemon. You also have, barring Charge Beam, no way to boost your SpAtk on this set, so maximize your damage output and ensure you can get your boosts & attacks in before your opponent can hit.
As written, this set can work well on most teams. Fast sweepers appreciate their checks and counters being worn down, while other walls can make your opponent struggle to break you.
EDIT: In doubles, really shines alongside fast-but-frail offensive Pokemon, as you're easy to ignore until you're the last Pokemon on the field with maxed out boosts to Def and SpDef.
Not a lot. Changing up the Plate allows for Flash Cannon (Clefable) as a coverage move, and also changes what you can wall/struggle to wall. Pixie Plate is arguably the best as you hard-counter Giratina, Palkia, and Rayquaza, as well as Yveltal, Zygarde, and Zekrom once they're legal. Flying is also an option, as it frustrates Groudon and makes every Earthquake carrier a free switch-in. The others by and large only counter specific threats and aren't very versatile for this defensive build. Physical builds are possible with Arceus' movepool, but not recommended due to the reliability of Judgment.
~Immune to Poison, Sand, and may as well be immune to Burn.
~Strong SpAtk means nothing can treat you as a passive threat.
~Strong Spd means you can get your boosts up & do damage (or set Stealth Rocks) without taking a hit first, a common weakness of defensive walls.
~Resist most attacks.
~Insanely high movepool means your opponent won't know how to counter for a few turns.
~Cosmic Power is very underrated.
~Until more Fairy-types are made legal (like Xerneas, for whom this set was originally designed to counter) to fight BD/SP Pokemon, Steel is a terrible offensive type.
~Few Pokemon are hurt more by "Four Moveslot Syndrome" than Arceus; this build has options that more passively defensive Pokemon would kill for, and the stats to go full-passive if desired while still dealing more damage than passive Pokemon can imagine...but you can't run everything you need.
~You don't get Taunt or Toxic without transfer. Taunt can shut down would-be counters who need to set-up first (with your high Spd, you should always shut down set-up sweepers) while Toxic puts two of your worst counters on a timer.
COUNTERS AND CHECKS:
~Groudon and Ho-oh both only need fear Toxic and Surf. Ho-oh is arguably better, because of Regenerator and fears fewer of Arceus' coverage options.
~You can't hurt Skarmory much 9/10 of the time, but Skarmory can't hurt you near at-all. Once Arceus can fight against Gen V+ Pokemon again, Celesteela and Corviknight are the same headache as Skarmory.
~Offensive Dialga sets can muscle through with Earth Power and Aura Sphere, while only fearing your own Earth Power (or Focus Miss).
~Steel types in general can block this moveset's damage, while knowing Arceus can't run coverage to hit every Steel type in the game. You still have Recover, though, leading to a long, drawn-out stall match if they don't have a strong Atk/SpAtk.