Ideal team formation:
-- Absol + 3 teammates
---- I personally recommend Typhlosion, Swampert, and Latios. Reasons below.
-- Absol being level 50-59 is the lowest I'd recommend; it will give you a 10% boost. More on recruitment rate below.

Ideal moves:
-- Absol: Bite and/or Thief, any combination of TBolt/Ice Beam/Flamethrower
-- Teammates: Variable attacking moves, preferably with some range.

Ideal item array:
-- Get Absol to have the TRAP SEER and SUPER MOBILE IQ skills.
---- This will eliminate the need for the No-Stick Cap and the Mobile Scarf.
---- Because of this, Absol will be able to carry the X-RAY SPECS without issue.
-- Either do not equip your teammates with items, or give them Oran Berries. This means that, when dismissed, you will neither lose anything of importance nor clutter your inventory with their items.

-- Toolbox:
---- Spare Friend Bow
---- 99x stack of Gravelerocks, or as close to 99x as you can get it.
---- Music Box
---- 4 Huge Apples
---- 4 Max Elixirs
---- 4 Reviver Seeds

This will leave you with 15 items, out of a maximum of 20. My personal recommendation is to fill the last 5 slots with an emergency Escape Orb, one or two Cleanse Orbs, and fill the rest with Reviver Seeds. The Escape Orb is not necessary, but useful if you get into a tight spot. The Cleanse Orbs are to account for the 5% flat rate of items you find in Buried Relic being sticky.

How to play each floor:
-- Play normally until defeating Registeel on floor 35, then dismiss your teammates.
---- This is to ensure the Regis do not attempt to join you, because you don't want to risk them KOing Mew and it's just generally cleaner to not let them attempt at all. They have a very low recruitment rate, but it's comparable to Mew's, so it's best to be safe.
-- From floors 36 to 98, comb the entire floor while watching for Mew. Pay close attention to any Pokemon that seem to be ignoring room and hallway walls, as Mew can go over water. Move to the next floor when you're reasonably sure Mew hasn't spawned.
-- If you're sure you've found Mew, equip the Friend Bow and KO it.
-- If you find Mew and KO it, but it does not join you, move on to the next floor as Mew will only spawn once per floor.
-- On floor 98, skip turns near the stairs for as long as your comfortable to give Mew extra time to spawn. At the second or third "Something's stirring" message, either move on to floor 99 or use an Escape Orb.

Notable annoyances and threats:
-- Shedinja: 26 through 39, skipping 35. Defeat with Gravelerocks.
-- Sandshrew: 36-59. I don't know why that's a threat but it is.
-- Ditto: 16 through 34, skipping 25.
-- Wobbuffet: 19 through 24.
-- Shiftry: 68 through 74.
-- Machoke: 80 through 87.
-- Haunter: 82 through 93. Can be easy to mistake for Mew because it ignores tile passability.

Recruitment modifiers:
-- Mew's base rate ir 0.9%.
-- At level 50, you gain a 10% boost. At level 90+, you gain a 24% boost.
-- The Friend Bow gives a flat 10% boost.

Remember that the party leader must both deal the finishing blow and be adjacent to the target in order to recruit in the generation 3 games.

This means that ideally, your likelyhood of recruiting Mew upon KOing it will be anywhere from 20.9% to 34.9% depending on level.

Mew spawn rate:
-- 36-39: 0.9%
-- 40: 0.62%
-- 41-59: 0.41%
-- 60: 0.62%
-- 61-64: 0.41%
-- 65-67: 0.31%
-- 68-69: 0.21%
-- 70: 0.26%
-- 71-74: 0.32%
-- 75-81: 0.66%
-- 82-87: 0.44%
-- 88-90: 0.66%
-- 91-93: 0.62%
-- 94-98: 1.23%

Don't ask me what's with these numbers because I have no idea.