If I understand "Save for Web" correctly, the process optimizes the photograph for web display. This would include converting to the sRGB color space too.
I tend to always shoot at the highest quality possible (in my case, RAW). This allows me to have the most options with my photos. If there is a photo I want to add to my website, I follow this workflow:
1. Convert from RAW to a 16 bit image.
2. Do any necessary processing and cropping.
3. Convert to 8 bit mode.
4. Adjust image size to 72 dpi and pixel dimensions to desired size.
5. Save for web
Depending on quality level chosen and picture detail, I end up with a photo that is usually somewhere between 15K nd 40K. This gives me a photo that will display well on the screen but will not print well at all, preventing someone from hijacking your work and printing copies for themselves. It also allows faster page loading.
If I know that I am shooting a family event like a birthday party for the kids, then I will shoot in JPG mode, usually small and fine quality. This lets me make a 4x6 print if someone wants one. I still prepare the images for the web by converting to 72 dpi and saving for web. Again, pages with a lot of images will load quickly.
As always, the screen shot will not show the detail of a print.