Save for web does just that; it makes a very small file suitable for web use. Jpegs have larger and smaller file sizes depending on quality; ie how much interpolation is being made.
It's fine for graphics for a website, but you should use save as jpeg and dial int he quality you want to get a quality file. This also saves exif info, which "save for web" strips as well.
I've gone to using Flickr, as they have an amazing algoritum that seems to make small file sizes and jpegs in various sizes available that are as good as the original.
My workflow is to open in RAW, save out as PS or Jpeg, then upload the jpeg to flickr and either link or download a small sjpeg for use elsewhere.
Browse around on Adobe.com's tutorials, forums and other info. CreativePro.com also has great tutorials.
A copy of Real-World Photoshop, or Real-World Camera RAW is a good investment. Bruce Fraiser is a heck of an author, IMHO.
Jack