I am suprised nobody has mentioned this before. There are superior image saving techniques than Photoshop. You can mess with Adobe exporting for days and you will get much better quality with different tools. Lot of times you save 60% more while having identical image quality.
If you optimize the images in a good way, you will find that JPEGs are good for photos and PNGS for mostly everything else. Its good habit to always optimise images, its really simple and it you will save lot of bandwidth / diskspace.
If you care about sizes and quality i highly recommend ImageOptim its free which with Jpeg, PNG and Gif images. It does a lot of clever optimalizations (cleans up headers and metatags) and it just makes all images a lot smaller. Its loseless so even if you use jpeg it wont change the image quality. You should use lossy compression on jpeg and then run it through ImageOptim.
Photoshop save for web isn't really good for saving compressed images. There is paid (unfortunately) program called JPEGmini. Its hands down best lossy JPEG compression engine. I would suggest export from your program as high quality jpeg then run it through JPEGmini and then run it through ImageOptim. It makes insane difference.
ImageAlpha is also free project that applies lossy compresion on PNGs. This is very useful when you need small transparent images. Again the workflow would be export PNG24 then run it through ImageAlpha and after that ImageOptim. You might ask why you would need lossy PNG. Well if you create graphics for webs, interfaces or sprites for games for example. It is extremely important to have small transparent images.
If you want loseless PNG just use ImageOptim.
When you put stuff on web, its good to know about progressive loading. Images are loaded as a whole and at first are blury. This is very useful for user experience. Both Jpegs and PNG can do this but its more effective for Jpegs. More about progressive loading it here.
All of the software above is unfortunately only for Macs. Probably because most of web developers and designers have macs. If you need something similar for Windows i've heard good things about FileOptimizer which uses many of the same techiques as the software mentioned above.