"how do I go about deciding which textbooks to read in a particular subject,"

You probably know this anyway Qiaochu, given your involvement in the various math stackexchanges. But others here might find it useful.

This is my Google search string for mathematics textbooks on the stackexchanges:

"coding theory" books | book | reading | texts | list | "reference request" site:math.stackexchange.com | site:stats.stackexchange.com | site:mathoverflow.net | site:crypto.stackexchange.com | site:quant.stackexchange.com | site:scicomp.stackexchange.com | site:cstheory.stackexchange.com | site:cs.stackexchange.com

Replace "coding theory" with the area you want to learn, and you end up getting a nice list.