sRGB is the way to go.  Adobe's proprietary RGB has, theoretically, the
ability to compress more colors into the same space, but it requires special
software to display properly.  Any misstep, and your reds and magentas will
look really dingy by comparison.  Are you absolutely certain that you were
not saving in Adobe RGB at any point in your workflow?  That might account
for less-than-expected results.

Since you don't have any control over the destination viewing conditions
you can't assert your intentions. The best you can do is ensure the
image looks OK without colour management on your monitor, or on the
"typical" monitor. What it will *actually* look like on the user's
monitor is anyone's guess.

Stick with sRGB, then I think your options are a) soft proof with the
profile set to Monitor RGB, which will show you how the image looks on
your monitor without colour management; b) soft proof with the profile
set to Windows/Mac RGB, which will show you how the image looks on the
typical Windows or Mac monitor; c) if you're using Save for Web, click
the "Preview in..." button before saving to ensure it looks as you wish
in the browser; d) turn off colour management in the Color Settings dialog.

You can control what you post on your website but not how it is seen or
displayed.

Assuming that your monitor is "calibrated correctly, sRGB is the standard
for web applications.
Photoshop si usually set by defaut to use Adobe's wider color space. This
should produce different results when an sRGB image is used.

I am NOT anything close to a color expert, so believe what your read here
at your own risk!  :)

IMHO an embedded color profile like sRGB makes no difference whatsoever to
a non-color-aware program like web browsers.  I also think that most
aspects of "correctly calibrating" a monitor deal only with building a
monitor profile that allows colour aware applications to display the
correct color within that color-aware application software.  For non-color-
aware applications like web browsers, the only two parts of monitor
calibration that affect the appearence of images are the white point
setting and the gamma.  The rest of the calibration process is useless for
non-color-managed applications.

I believe that the reason two images may look different in two different
browsers on the same computer has to do with how the browsers handle the
dithering required to get images to match the browser's color palette.  I
don't think it has anything to do with embedded color profiles.  Internet
Explorer has a 212 color palette.  Netscape has a 216 color palette.  Each
browser has its own color palette.  When browsers encounter colors in an
image that are not available in the browser's palette, then the browser
dithers the image to make it match the available palette.  If the image
that you post to your web site has already been converted to the Internet
Explorer color palette, then people who look at it using IE will not see
different colors do to dithering. Even if you do this pre-conversion,
people using other brands of browsers will still see imges that have been
dithered to match the color palette of their browser.  And of course, their
monitors may still have a different gamma setting and a different white
point.  There is nothing you can do about these things.  There is no
"correct" white point, although 6500K is very common and most PCs use a
gamma of 2.2 but makes generally use gamma 1.8.

Anyway, that's my 2¢.