Personally, I've just started reading Hocking & Young (Shocking and Fun!) and it seems quite good so far.
I've made some substantial progress in _Counterexamples in topology_ and it's really good... It's not really a textbook, just a thing booklet that goes over general topology, then goes through a lot of examples and provides all these really nice charts of topological spaces based on properties. I actually made a graph, mostly based off it:
http://christopherolah.wordpress.com/2010/03/09/compactness-...
Oh, and Needham's _Visual Complex Analysis_ (in list) is awesome! Best math book I've ever read.
Munkres is okay – pretty readable, gets the job done, has enough interesting problems. I like Hatcher’s book though, so his recommendations (your first link) are probably solid.
Personally, I've just started reading Hocking & Young (Shocking and Fun!) and it seems quite good so far.
I've made some substantial progress in _Counterexamples in topology_ and it's really good... It's not really a textbook, just a thing booklet that goes over general topology, then goes through a lot of examples and provides all these really nice charts of topological spaces based on properties. I actually made a graph, mostly based off it: http://christopherolah.wordpress.com/2010/03/09/compactness-...
Oh, and Needham's _Visual Complex Analysis_ (in list) is awesome! Best math book I've ever read.