When it comes to strategy I am probably the worst at it, which is probably why I don't battle competitively. However, that doesn't stop me from making the attempt to maximize my Pokémon's stats and having fun with it. Pidgeot is pretty fun to figure out, so here's a few things I like to do with mine.
The first thing I like to do is find the Nature I want. I like looking for one with either an Adamant (increase to Attack, decrease to Special Attack) or Jolly (increase to Speed, decrease to Special Attack) Nature. Most times though I like to go with a Jolly Nature as Speed is Pidgeot's best stat. Another thing to keep in mind is the Pokémon's characteristic as that can have an effect on stats too, albeit in a minor way. I think something that boosts its HP, Speed or Attack would be good. Most times though I just don't bother with it.
Something I like to make some use of is the Super Training. Though it can be a bit time consuming it helps a ton to get those EV's (effort values) into the stats you want. I use it to up Pidgeot's Speed, Attack, and HP. I'll also use it boost its Special Attack a little bit as I plan to use Mega Evolution which makes use of its Special Attack stat, making attacks like Hurricane and Twister more desirable. However, if you don't plan to use Mega Evolution it would be better to put those EV's elsewhere.
Another thing to look into is breeding. I don't do much of it personally, but it is good to do for getting moves Pidgeot cannot otherwise learn on it's own––like Brave Bird and Feint Attack––and there is also the chance of getting Pidgeot's hidden ability, Big Pecks, which prevents its Defense stat from being lowered. If breeding isn't your thing there is also the DexNav app in Pokémon Omega Ruby/Alpha Sapphire which has a chance of finding Pokémon that know bred moves or have the hidden ability. Definitely worth checking out.
Depending on whether or not I plan to use Mega Evolution will determine what moves I will teach my Pidgeot. In Pokémon X where Mega Evolution is not available for Pidgeot I teach it moves like Fly, Return, Twister, and Thief. In Pokémon Alpha Sapphire where it is available I teach it moves like Aerial Ace, Twister, Return, and Hurricane. Not that much different really, but yeah. I need to work on it.