Mew - Fast Move

Giving him Shadow Claw would make him a mid-tier Ghost killer.
That's it really. Unfortunately there are no Psychic, Fairy, or Flying quick attacks to make him useful against Fighting or Poison

The Mewveset article on this very site is a good resource

I have psychic also, but I plan on changing it when I get a chance. I did spend a lot of fast TMs to get shadow claw which is one of the most ideal fast moves.

Probably not the consensus vote, but Charge Beam is pretty good for Mew, because electric is a fairly neutral type, and it generates energy faster than any other Mew move.

I did a quick plot of all the mew moves, graphing DPS against EPS, and the Pareto frontier running along the outside (optimal combination of DPS/EPS) consisted of, from highest EPS to highest DPS:

Charge Beam
Infestation
Snarl
Pound
Poison Jab
Dragon Tail
Steel Wing*

Steel Wing represents a significant drop-off in EPS for a very small gain in DPS vs. Dragon Tail. Shadow Claw fell just below Poison Jab, with a tiny bit less DPS, same EPS. Of the rest, Frost Breath was near Pound.

Snarl is also a good choice, with Dark being a fairly neutral type, but it doesn't pair well with Psychic.