The official web standards say that images are expected to be in the sRGB colour space.
In reality hardly any web browsers do colour management and convert it to the profile of your display, so you're stuck with trying to find a colour space which is a good approximation for the average monitor out there being used to look at your web pages. Luckily this was one of the design goals of sRGB so it's your best hope.
If you don't convert your images to sRGB they will look subtly different to what you would expect (but in the end sRGB is not an *exact* match for everyones' screens so it's a crap shoot anyway). To see the effect of not converting your image, in Photoshop try previewing the effect of assigning sRGB to the image.
should i process in RGB 1998 and then convert to SRGB at the end or does it make no difference
A common workflow is to process the image (colour casts, cloning out dust, etc, etc) to produce a master version at full resolution, and then produce downsized and sharpened copies for various uses (e.g. prints, web) from that master. If your master is in sRGB then you won't be able to take advantage of the wider gamuts of some output devices, even if a colour in the original was more vibrant than would fit in sRGB (and most dSLR sensors can capture a wider range of colours than will fit in sRGB).
I think most "serious" photographers use larger colour spaces (mostly AdobeRGB 1998) as it lets them take better advantage of the gamut of various devices without restricting their images to a specific gamut from the start.
Mostly I use AdobeRGB 1998 as my workspace, but my workflow for generating web images involves a Convert to Profile (sRGB) step, just as my workflow for prints involves converting to the printer's profile.
Did I mention I conduct Colour Management training?