Mew is an incredibly diverse pokemon. I have a set I've taken a liking to:

1st set: Baton Passer

Mew
Ability: Synchronize
Nature: bold
Item: lum berry/ weakness policy/ focus sash/ lax incense
Baton pass
Swords dance/ nasty plot
Rock polish
Double team/ taunt
252 hp 158 sp defense 94 defense

This mew is all about support. The item is up to you- lum berry heals any sp conditions your opponent may pile on you while your setting up, trying to disrupt your baton pass. weakness policy is nice if you get hit by a super effective move and survive- your offenses rise sharply and then you switch. Focus sash is probably the least necessary but can be useful. Lax incense is a mist have for double team sets. Although this set is mostly up to you, there are two moves you must have on it: baton pass so you can pass your stats on to another whole pokemon so it can enjoy them. Rock Polish gives mew the speed it needs to baton pass. Swords dance or nasty plot really depends on your strategy- is your team sp or physical? Put the corresponding move depending on the needs of the team. The last move depends on where you are using Mew- evasion moves are banned in a lot of official competitive battles, but it's very powerful, allowing mew to set up its stats almost without worry of being hit. Taunt is the option for official competitive play. When opponents see mew setting up, they might think they can set up there dragon dance rayquaza or geomancy Xerneas or swords dance garchomp and the like. When Mew has taunt however, the opposition is in for a nasty surprise. The real fear of this set is if it gets taunted, making it useless. This is why mew has to taunt before it is taunted, which is why rock Polish is so vital to this set. If your opponent has a prankster pokemon out however, you should probably keep mew far away due to priority taunts and statuses.