What should be done when no more Pokemon can be caught? (when full storage)

Unless you're collecting one of each pokemon in your active inventory, there's really no need to hang onto every single one of them. Technically the only ones you ideally want to keep are those with the highest CP, those you intend to evolve, and those you have a sentimental attachment towards. Your pokedex keeps track of all pokemon you've caught and seen.

I would recommend using the following guidelines to keep your pokemon inventory nice and organized:

• Sorting by CP, is the pokemon in the top 6? Keep them for battling gyms. The only exception here is rare pokemon that you're attached to and are willing to invest the large amounts of stardust to increase their CP as you level up.
• Do you have enough candies to evolve a pokemon? Great, keep one for when you use a lucky egg. Transfer the rest. For common pokemon like Pidgeys, transfer all except the number of candies you have divided by 12 so you can use up all the candies and evolve them for XP.
• Do you NOT have enough candies to evolve a pokemon? Transfer them, and get a candy. You're going to need more of that pokemon to evolve them anyway, so you can evolve them when you get enough candy.

If you stay on top of this, you should only have 6 battle pokemon + however many pokemon are ready to evolve. And if you use a lucky egg, ultimately an ideally organized trainer only needs 6 pokemon, as the rest can be transferred for candies.

I don't recommend buying more space, since you don't need to keep extra Pokemon around. The mechanic of candies being available by trading Pokemon even seems to discourage such hoarding.

To keep my bag from getting full, I sort by # rather than CP, and transfer anything that is duplicate. When I sort by #, Pokemon with the same number appear to be de-facto CP-sorted (perhaps you should sort by CP, then change to #, if it's not inherent behavior).

I tend to keep one of each stage of evolution, so for example I have a Pidgey, Pidgeotto and Pidgeot. I do this considering trading in the future, but that's up to you. I also actually tend to keep a hand full of Pidgeys, which I evolve all at once when I'm using a Lucky Egg.

You might have other little tweaks like that, but I do advocate sorting by # and using that metric rather than sorting by CP, unless all you care about is battle.

Other than buying more storage space, you can transfer your useless Pokemon (low CP) for candy which can be used to evolve tier 1 Pokemon for efficient EXP gain.

Unless you are planning to use the candies for evolving a Pokemon for gym battling, you should evolve a Pokemon you will transfer whenever you are able to to save space.