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.).
Fandom Fest 2014 cosplay: GLaDOS (Portal), Ellie (The Last of Us), Lara Croft (Tomb Raider 2013)
MCM London Comic Expo cosplay: Oktavia von Seckendorff (Madoka Magica), Fem!Slenderman,
Future cosplay: Faith Connors (Mirror's Edge), Lara Croft (Rise of the Tomb Raider), Tetra (The Legend of Zelda: Wind Waker)
2015 conventions: Anime Los Angeles, Anime Central, Japan Expo