After you've gotten your Basics down, the next order of business is to evolve them. This is where this category of cards comes in.
These are the standard Evolution-searching Supporters.
Professor Elm’s Training Method is more common, as decks usually use evolved ex's. If your deck doesn't, Celio's Network is strictly better, as it can get Basics in a pinch.
Holon Researcher searches for a δ Pokémon. It also has the utility of being able to grab a Metal Energy, though not all decks that play Holon Researcher also play Metal Energy.
Rocket’s Poké Ball searches for a Dark Pokémon. Unlike most of the other options, it is a regular Trainer, not a Supporter.
Poké Ball and Master Ball can get any Pokémon, even Basics, but are luck-based.
Usually only used in decks that have a strong card-drawing engine, the idea being that if you can draw a lot of cards, you won't mind the unreliability of Poké/Master Ball, as you can play multiples of those in one turn.
If the game is still in the early stages and your opponent hasn't gotten an offense going yet (or you have a comeback card to punish them if they do), you can evolve your Pokémon slowly by attacking with Make a Wish.
Make a Wish is an out to Trainer locks stopping you from using Rare Candy or Rocket's Poké Ball.
Unown M is generally inferior to Jirachi, having less HP and needing Psychic Energy specifically, but it can Shuffle into other Unown forms.