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Trainer
Its all well and good catching pokmon, but you need to have your trainer hit level five as soon as possible so that you can start training at gyms. Youll also stumble across more powerful pokmon at higher levels, so dont invest in any of the little cuties until youve started getting a decent team together.

There are a number of ways for your trainer to earn XP. Each levels full XP requirement corresponds to the level number, so at 1000 XP, you finish level one and move onto level two, then 2000 XP later, you move onto level three which needs 3000 XP before you can hit level four and so on.

100 XP Pokmon Caught
500 XP New Pokmon
10 XP Curve Ball
10 XP Nice Throw
50 XP Great Throw
100 XP Excellent Throw
50 XP Checking in at a Pokstop
100 XP Battling a Pokmon Trainer at a Gym
150 XP Beating a Pokmon Trainer at a Gym
50 XP Beat a Pokmon in training at a Gym
200 XP Hatch a Pokmon
500 XP Evolve a Pokmon

Using items like Incense and Lure Modules is a good way to boost the frequency of Pokmon popping up on the map. Walking around checking in Pokstops is also a good way to get both XP and items, particularly as they refresh every five minutes.

And if youre low on pok balls, dont waste XP capturing duplicate Pokmon unless youre particularly enamoured with their CP.

Hitting pokmon inside the capture ring at its smallest will earn you XP for skillful throws. Move the pok ball in a circle before you throw it, and release when it starts to sparkle to get a curve ball. The throw bonuses dont seem to stack so focusing on precision is the best way to gain XP with throws.

You should hit level five in no time.
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Pokmon
When deciding which Pokmon to level up, its best to choose the ones with the highest CP. To increase their CP, you need to power them up, and to power them up you need Stardust and Pokmon Candy for that particular variety of Pokmon.

Stardust can be used to power up any kind of Pokmon. You can collect it by capturing Pokmon and hatching eggs.

Pokmon candy is awarded for catching Pokmon, hatching eggs, and transferring Pokmon to the professor. You cant get them back once you send them away, so if youve got a butt ton of Drowzee, get rid of the lower level ones to bump up the candy you need for powering up and evolution.

At the moment it seems that the end stats for your Pokmon will the same regardless of whether you power up to the max or evolve first, and the Pokmons size will have a bearing when battling other Pokmon with a similar CP. But if youre keen on taking over all of the local gyms, CP should be your focus at the start. Because CP represents the Pokmons strength, a higher stat means its moves will be more powerful.

Evolving your Pokmon will also give its CP a significant bump. If you want to evolve as soon as possible, then catching the same species of Pokmon is what you should be aiming for, as you can hand them over to the professor for the candy you need to evolve them.

Its worth noting that your trainer level will affect the available CP of your pokmon, so you may hit a wall with powering them up until your trainer level increases.