Foolestroupe, what you say on breathing and posture sounds good, and is also akin to Alexander Technique teaching: it's also good for singers and musicians. Like many things a lot of singing comes down to 'mental tricks' (such as 'thinking' the voice in the top of your head, or end of your nose for higher notes), and it's a case of finding what works best for you. I can't recommend too highly finding a good singing teacher.

A good tutor book, with lots of exercises and the reasons why, is George Dodds' 'Voice Place & Training Exercises' published by Oxford University Press. It comes in two versions for different vocal ranges: Soprano & Tenor and Alto & Bass. It's quite an old book, although still in print, but very sound. It's possible to work through on your own, although it is undoubtedly best with a teacher.