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You should set ProPhotoRGB 16bits as the color space for photo shop. If you also end up saving an sRGB copy then you can see what does when you use the convert to profile tool and toggle it on and off (Although on a non-wide gamut monitor you really won't see much of any change most likely, you could go to proofing and set sRGB as the target and then set out of gamut warning and see what areas get lit up).
I'd recommend you do all your editing work in ProPhoto (that's the color space that Lightroom uses, btw). When you make web copies, convert the profile to sRGB. Someday the world will be filled with monitors that can display AdobeRGB, or maybe even ProPhoto or something similar. By then, all web browsers will be color aware and we'll keep the same profiles for all our new images, whatever their final destination. For now, we have to work in a large color space, print in it when we can, and convert to narrower sRGB when we want to display on unknown devices (such as the web). Just don't get caught embedding your own monitor profile in your images. It's there to correct for your monitor's imperfections.