For images going to the web, process them using the sRGB color space, but you don't really need to include the color profile with the image.
Standard web resolution is 72 dots per inch for an image. As long as you set the width & height to what you want, the actual dots per inch isn't really important when viewed in a browser. But for printing the dots per inch is very important. If you have an 800x800 image that you want to print, dots per inch determines how many of the 800 pixels will put printed into a one inch of photo paper. At 300 dpi, the image will print 2.667 inches x 2.667 inches. At 72 dpi, that same image will print 11 x 11 inches, but will be much lower quality.
For the web, we want to maximize quality and minimize file size.
Whatever size you want the image to be displayed on the internet is the size you need to set in photoshop. If you upload a file and have the web page display it as a different size, you will see a dramatic quality loss as the browser does a hack job of resizing the image.
For the web do the following:
-save the file as an 8-bit jpg file
-use the sRGB color space
-resize the image to the proper dimensions using Bicubic Smoother (enlargement) or Bicubic Sharper (reduction)
-choose Save For Web & Devices and save the image as a jpg, reducing the quality to the minimum level that still looks good, tweak it a tad with the blur setting if it looks crunchy
- in the Save For Web tool, uncheck ICC Profile to reduce the file size
- you may also set the image size within the Save For Web tool, but it loads pictures slower if they are larger, so its faster usually to change the image size before loading it into Save For Web
I usually edit pictures differently for the web than for printing by adding more saturation and contrast.