Which book on complex analysis is good for self study?

Nice link ;)

• Visual Complex Analysis (Tristan Needham)
• Visual Complex Functions:An introduction with phase portraits (Elias Wegert)

Enjoy Them...

Gamelin is quite good. After or together with it, I recommend you to read the following.

• Reinhold Remmert. Theory of complex functions. Springer 1991.

Then there is the second volume:

• Reinhold Remmert. Classical topics in complex function theory. Springer 2010.

Gilman, Kra and Rodriguez, wrote the excellent book "Complex Analysis in the Spirit of Lipman Bers". It has everything you need to study complex analysis and has great exercises.