re shooting in Raw and converting on computer - that's pretty much the standard "workflow". A friendly program for doing this is Google's Picasa, which is free, while for more Pro work you'd look at something like Adobe Camera Raw. Both do non-destructive editing, so your Raw files remain unchanged, like film negatives, and the JPEGs you create are the "prints".
Historically, a good Portrait lens has been a prime (non-zoom) lens in the 85 - 110 mm range, but with the smaller APS-C sensors in these cameras, the equivalent is 50 - 80mm. (I don't know what Nikon has in that range, though, or whether that camera can handle old lenses.)
Filters: there are things some filters can do that you can't replicate on the computer. One is a Polarising filter, to reduce glare from e.g. water. Another is to use a graduated filter to e.g. darken a bright sky. In both cases it's not just an effect, it prevents part of the image "blowing out" and lets you capture more detail from darker areas of the frame.