There are 22 different poke personalities and these give a stat bonus as well as a stat reduction or sometimes nothing at all to a poke.

Personalities can make a huge difference late game if your trying to min max you stats but it can ruin some potentially too. The idea is to have a -10% on a stat your poke doesn't benefit from.

If the poke is a Physical attack user then ideally having -10% Special attack is perfect and either +10% Speed or Physical attack. In this case cheerful or modest are the best options.

Personality Stat 1 Stat 2
Bold P.atk -10% P.def+10%
Brave P.atk+10% Spd-10%
Calm S.patk+10% Spd-10%
Candid Neutral Neutral
Carefree P.def+10% Sp.def-10%
Careful S.patk -10% Sp.def+10%
Cheerful S.patk -10% Spd+10%
Composed P.atk -10% Sp.def+10%
Gentle P.def-10% Sp.def+10%
Hardy Neutral Neutral
Hasty P.def-10% Spd+10%
Immonsteruous Neutral Neutral
Lonely P.atk+10% P.def-10%
Mild P.def+10% Sp.atk+10%
Modest P.atk-10% Sp.atk+10%
Naive S.pdef-10% Spd+10%
Naughty P.atk+10% Sp.def-10%
Sassy Sp.def+10% Spd-10%
Serious Neutral Neutral
Stubborn P.atk+10% Sp.atk-10%
Timid P.atk -10% Spd+10%
Rash Sp.atk+10% Sp.def-10%

These are the best Personalities for Popular Poke

Arceus: timid

Ho-oh: cheerful or stubborn

Dialga: modest or timid

Palkia: timid or modest

Celebi: timid or cheerful

Zygarde: cheerful or stubborn

Rayquaza: modest or timid

Tornadus: timid

Regigigas: cheerful or stubborn

Regice: timid

Kyurem White: modest or timid

Kyurem Black: cheerful or stubborn

Deoxys: modest or timid

Kyogre: timid

Groudon: cheerful or stubborn

Tapu Lele: Timid

Lunala: Modest or Timid