My preferred and recommended sets go as:
Shadow Claw/Dragon Tail + Dragon Claw
Shadow Claw/Dragon Tail + Psyshock
These are dodge-friendly, and fun sets to use.
Currently I’m running DT+DC, but would like Psyshock eventually as it outperforms Dragon Claw and has generous timing and is not resisted by most META gym defenders. I simply enjoy Shadow Claw more than DT, and it is faster, but is resisted by the META defenders.
I feel like Mew should use moves with as many neutral matchups as possible since there are normally better options for specialization. Dragon moves are also super effective to the Lati-twins, so in larger groups Mew can be used there to some avail.
For more serious matters, there are better options all around. Mew is more of a fun Pokémon to use than a powerhouse for anything in particular. I wouldn’t worry too much about min/maxing here
Also, the sets I mentioned do at least 89% of Mew’s highest dps:
DT+Psy - 98%
DT+DC - 90%
SC+Psy - 96%
SC+DC - 89%