Thanks to everyone who gave me hen advice. I think I've finally settled on four new birds: A Columbine (hybrid), a Light Sussex, a Welsummer, and a Wyandotte. It was really hard to decide which birds would fit in well with our current lot, and which are happy enough to live in a large run.
Being in Scotland, I'm a little limited in that there doesn't seem to be a large number of breeds available, and to get to them, one has to travel quite a distance. So I began looking at what was available close by and worked backward from there. While searching for information on the various breeds, I found this handy reference. It gives a good overall picture of each breed and tells you about its general personality. If you're undecided about which hens to choose, please do have a look. It helped me a lot.