Mode I and III are both sRGB, but I is tweaked for portraits and skin tones while III will give you better greens (more vivid colors for nature shots). Mode II is a wider gamut allowing for more true to life colors. To avoide problems with Photoshop messing your files, select Don't color manage when opening the file. Then go to the Menu Image, Mode and select Assign Profile, choose Adobe 1998. Before publishing you file to the internet you should convert it to sRGB since the browsers can't handle Adobe 1998 and the colors won't look right.
>I can't really tell you the difference between Mode I and >III, but I can tell you this. Unless you are opening your >images in Adobe Photoshop, and abiding by the color profile >information, OR opening your images in Nikon Caputure and >passing them to Photoshop, you should avoid mode II. It >assigns a profile for Adobe RGB(1998) colorspace, and that >will make colors look dull when viewed in any non-ICC-aware >application (or Photoshop, if you don't handle the profiles >correctly).