Digital BW, The Print

Hi,
I am working on re-sizing images for the web and am having some difficulty
Which I am hoping some-one can advise me on.
A number of you gave me some very helpful feedback which I followed and then
ran into a conflict.
The company that I am working with apparently uses up-load software that
essentially does what PS does and they therefore asked that I just re-size
the images at 500 pixels high using the following method.  Using the image
size in PS, check the boxes:  Scale styles/constrain proportions/resample
image and change the pixel height to 500. Voila,  the resulting image after
said adjustments fell as follows: ( Doc size: 2.31x1.52 at 329 res/761x500
pixels)  While it all seemed easy enough  I had sincere doubts about the
resulting image.  When I checked it on the web, it looked dreadful, flat as
a pancake and bore no resemblance to the image on my screen.
Although I have tremendous faith in who I am working with re: web technical
stuff, I am not too sure about the actual imaging aspect of it.  I have far
more faith in the group over here.  So,  it would be wonderful if some-one
could point me in the right direction. Or, the question may be is the 500
pixel high requirement ridiculous.  The one thing I did notice was that the
file size requirement just had to be under 2MB.  The methodology for getting
there was just suggested as the easiest especially as their software did
what P.S. Did and that should probably not be done twice.   My images are of
varying sizes therefore surely just using the  set 500 H pixel change on
everything is going to result in widely divergent results.
Thanks for any guidance.  Siobhan