Generally speaking the "accepted" embouchure is placing the mouthpiece 2/3rds on the
top lip and 1/3rd on the bottom. The position of the lips should be compressed into a
position half way between a whistle and a smile. The chin should not push up (bunch)
although the jaw should drop gradually when descending to the bottom register.
It should be and feel as natural as possible and when suitably developed capable of
playing a four octave range without changing the position of the mouthpiece. It should
be capable of playing a "long note" on every pitch from Top C to at least pedal E or D
without undue strain or pressure, and slur a three octave passage without contortions.
An "acceptable" embouchure is one which can achieve the above although it may not
conform strictly to what I have described - "if it works leave it alone".
Pushing the chin up presses the lips together and results in a thin squeezed sound and
other problems too many to mention including the lower lip sliding up behind the top.
Remember "free" buzzing is not the same as buzzing on the mouthpiece. Nothing
wrong with that as a warm up procedure but it's not the way you should play. I suggest
you read Cindy Lewis at embouchures.com who developed a problem through
chin bunching. Play a Top C on your mouthpiece and then remove it from the
lips still blowing - there should be no sound and a small gap between the lips.
Smiling embouchures should be avoided, the corners of the lips should pull down.
I am unclear as to what you mean by a "purse string" embouchure and also the
playing or not comment, perhaps you would care to elaborate