The Sh'moneh Esrai - or Amidah - is set up to be a T'fillah b'Lachash, a "silent meditation". The paradigm is taken from Hannah in Sefer Sh'muel I 1 - where her lips move w/o being audible. This most successful and heartfelt prayer was chosen by Hazal for emulation - particularly in the Amidah.
That the Amidah is primarily silent - seems to go without saying. Though - the truth be told - that some customs suggest raising one's voice a bit during the Yamim Nora'im and there have been rabbis who have davened quite audibly.
The Shulchan Aruch 101:2 suggests that the volume be loud enough so that one can hear one's own articulation with one's own ears, but NOT so loud as to disturb others.
The Ben Ish Chai in Parshsat Mishpatim disputes even this level and suggests total silence, with lips moving w/o any sound at all.
Here is how I see this dispute:
A The SA seems to take a Halachic approach that Amidah is prayer. Prayer requires articulation. Even Hannah moved her lips, suggesting after all that there was some minimal volume
B Ben Ish Chai is apparently following a more Qabbalistic approach. Those familiar with R Aryeh Kaplan's understanding of Amidah as the core to "Jewish Meditation" will readily see that total silence is "more meditation-like and less prayer-like". And in that case, an atmosphere of total silence would be preferable.
At any rate, proper decorum in shul during the Amidah is a MUST in order to create the proper atmosphere.