As a new member here, I just thought I would give you some thoughts on this. I'm not a scanning expert mind you, but I have been scanning things for many years. The idea, I think, is to always scan at the scanner's best resolution (it's real optical resolution that is, not an interpolated one), 300dpi output resolution (this is just a tag in the file that the printer uses - it changes nothing in the screen display), and at the same time, adjust the output or print size settings so that a print of the scan would be the same size as the original you scanned (usually, 100% magnification). Unlike with scanning a negative, there's no point in magnifying a print. Then, just adjust the image size in Photoshop Elements to whatever you like for displaying on the web (just plug in the number of pixels you want either horizontally or vertically, and the other one follows - for example, if a horizontal composition, anywhere from 500 to 750 pixels, and if it's a vertical composition, under 600, so that it will fit on a standard monitor).
You really don't need the full Photoshop to do the kinds of things you would do to a scanned print (sharpening, adjusted levels, adjust toning, spotting, cropping, etc.). The rest of the stuff in Photoshop is more useful to graphic artists, and to photographers who like to heavily manipulate the image (presumably, not many members here fit that category, including me).
If it's a B&W print, I scan it as if it were colour, and then, in PS Elements, I desaturate the master channel, rather than just using the "remove colour" or the "greyscale" commands. That way, it remains a colour image even though no colour is visible, and it can be easily "toned". If the original print has been toned, then of course, you have to scan in colour if you want to preserve the tone. The key is that, if the original is a B&W print, and you want to keep it that way, scan it in colour, but then desaturate the master channel in the colour settings (easily done in PS Elements).
I've also used Picture Window Pro, but it really doesn't present any advantage over PS Elements when working on scanned prints, in my opinion, and it's harder to use than PS Elements. If scanning negatives, it's a whole other story, though.