Should you power up your Pokémon’s CP first, then evolve? Or should you evolve your Pokémon, then power it up?
It’s important to note that your trainer level affects the CP of the Pokémon you see out in the wild. Your best bet is actually to catch the highest-possible CP of whatever Pokémon you’re looking for rather than powering up its CP manually with Stardust and candies, and it takes a higher player level to start catching those high-CP Pokémon.
Since the CP ceiling for wild Pokémon will keep getting higher the more your level increases, it’s best not to power up your Pokémon when you’re still a low-level trainer. This just wastes Stardust and candies that can be used more effectively on a fully evolved Pokémon, which will be stronger for having started out with that higher CP.
Ideally, you’ll level up by catching multiple of the same Pokémon and getting all those candies for it. Then, you’ll evolve a wild-caught Pokémon whose CP is already at least three-quarters of its bar, which will make its evolution that much stronger without using all that dust powering up a weak Pokémon first. Powering up the evolved Pokémon seems to be a better use of your Stardust and candies.
It is also worth noting that with each level increase, you will have to power up your Pokémon again because their CP ceiling will increase accordingly. Should you always level up your highest CP Pokémon? at page 2