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.).
Anime Midwest cosplay: Armin + young Armin Arlert (Attack on Titan), Madoka Kaname (Madoka Magica), Mayoi Hachikuji (Bakemonogatari)