Honestly, I'd save up and invest in a high quality wig. It'll be worth it, trust me.
As for which dyeing method to use, it depends on the wig's fiber type (kanakelon, hiperlon, human hair, etc.).
Matsuricon/Glass City Con/Youmacon Cosplay: Armin Arlert/young Armin (Attack on Titan); Ultimate Madoka (Puella Magi Madoka Magica); Fem!Masky (Marble Hornets)