Paul, please forgive me if this is all old hat to you, but even if it is it might be useful to some readers.
I use a hardware calibrated screen (ColorMunki Display). I don't really know what to say about those images because I don't know what they should look like, but have you looked at the
Lagom LCD test images? I think the
Black level,
White saturation and
Gamma calibration images are key. Ideally you should be able to make out Level 1 in the black image and Level 254 in the White image, and the rightmost of the Gamma charts should show as very near to 2.2. How well your screen does will depend on the calibration and the characteristics of the screen. The
Viewing angle and
Gradient (banding) images will tell you something about your screen too.
I found that when I calibrated my screen I could see more detail (good and bad) than before in my images.
I have found that using camera profiles in Lightroom has enabled me to reveal more detail in images. This involves photographing a Macbeth colour chart and generating colour profile(s) for use in Lightroom. I generate camera profiles using Adobe DNG Converter and DNG Profile editor, both of which are free.
I have found that using white/grey card reference shots to set white balance in post processing has helped greatly with getting colours rendered more realistically.
The combination of white/grey card white balancing and camera profiles has helped me deal with some quite difficult colours, such as some blue/purple colours that a lot of cameras seem to find difficult to cope with, and combined with the calibrated display this has let me render some of those colours in ways that even my wife, who is very colour sensitive, finds realistic (colours of flowers that she knows well. We had an example of that just this evening as it happens.)
I don't print often, and when I do I use a commercial printer. In Lightroom I generate the versions of the images I send to them for printing using the printer profile they provide. This way what I see on screen, what I see in the prints, and what I see real world all match up fairly well in terms of colours.
