Best for picture quality and best for web don't always coincide but if you will only view on computer (web) than you can stay in sRGB all the way through.
If you're doing heavy editing, pushing colors and dynamic range, you want the largest color space which is ProPhoto (16 bits). This is even if your only output is the web. Just as you want to edit in 16 bits to minimize data loss, you want to edit in the largest color space possible for the same reason.
You can then use "Save for the web" to do your conversion to sRGB.
It also confuses me. I was under the impression that most web browsers don't handle Adobe RGB very well and that regular RGB was best.
I'm going to try this.
All that means is that if you intend to publish to the Web, or print with a printer that only accepts sRGB, then you'll need to use the Edit > Convert to Profile > sRGB option in Photoshop. You can even write an action that does this automatically for you.
And because the Profile Mismatches options are not activated, you can still use ProPhoto RGB when transferring in images from Lightroom or Adobe Camera Raw and Photoshop will honor that color space.
