Once I have chosen a hue, how can I create a range of tints, shades and shadows?
You can't do it with GIMP in automatically way.
You can use some online tools or third party plugins.
Try Color Hexa ( http://www.colorhexa.com/ ), put your color in the search input and it returns color schemes, alternatives, shades and tints, tones and other useful related info.
Then you can create your palette in GIMP.