Stored Power is great if you know you can get off mor than 1 CM, otherwise I'd say stick to Psychic.
And for Nature, it probably depends on which Gender. Timid or Modest would be great for either really, but if you want a male, it might also be able to work with a Defensive nature, like Bold or Careful. Although if Meowstic-F it has crappy Sp. Attack, so I'd say Modest to give it extra power, as its speed is relatively fine.
And, because someone earlier in the topic wondered, Meowstic does get Swagger, and also stuff like Barrier and Yawn, and Attract (Which everyone seems to be against, its a great status) All priority.
And for Doubles it also gets Helping HAnd. Not really a quality to make it better than other pokemon for that role, but still.
I did get a Shiny Male, but it's a brave nature, without the Hidden Ability.
I did get a Modest Espurr who is now a Female Meowstic with Perfect IV in SpA, SpD, and HP, 29 Defense, and low 20's in Speed. So I maxed out IV's in SpA and Speed and Rest in HP. Thinking of a good moveset for her though. With those stats, think she can get multiple calm minds off? Or at least 1 calm mind and a charge beam or 2? if so...
w/Focus Sash/Petya Berry/Salac Berry/Weakness Policy
Stored Power
Calm Mind
Charge Beam
SHadow Ball
With Weakness Policy... if you can predict a weak SE attack, like a Weak Shadow Sneak, you can boost Stored power instantly to 100 BP. However, I wonder what are the chances of getting hit by a Weak Bug, Ghost, or Dark attack... Salac Berry may be best. Shame I didn't get COmpetitive... but I like the ability to go through Substitutes and the screens.
My Other Option
Salac Berry/Safety Goggles//CHoice Specs/something else
PsyShock
Shadow Ball
Me First/Calm Mind/Signal Beam
Thunderbolt
Me First Might be interesting with her above average speed... I mean sure, it's not the fastest Me First user, but it could be a very nasty surprise. But it's also unpredictible, and sadly I didn't get 31 speed... so even with max Speed IV's she won't be super fast
I do like the uniquess of the top one... it's just getting Stored Power strong enough which may be a pain... If only this was a Baton Pass team... but it isn't. Still, With Gourgiest inflicting W-o-W to everyone, she could maybe switch in on a weak Ghost, dark, Bug attack to activate Weakness policy... maybe...
There's no way female Meowstic will be getting much usage in NU, let alone RU. The best Pokemon in 5th gen NU was Jynx, which has 32 extra base Special Attack, a water immunity, a sleep move (when does anyone EVER stay in after they've been Yawned), Nasty Plot, and fantastic secondary Ice STAB over female Meowstic. Sure, Meowstic has 9 extra Speed, but Jynx's base 95 was the Speed benchmark in NU, and it should be even better with one of the few viable NU Pokemon faster than Jynx (Charizard) leaving NU for sure with its new Mega forms. The ONLY thing Meowstic-F has over Jynx is its ability to outspeed scarf Primeape with a scarf of its own. (Jynx speed ties it anyway) Seriously, that's it. I don't see any reason to use it over Jynx, Musharna, or any other good NU Psychic-type.
None of those Psychic's have the ability to pass through Substitutes, screens, and such... but you are right Female Meowstic doesn't have as much punch as Male one... which is a shame because I love the females Tsundere look. Still plan to use her on my second team.