Hi again - had to end last night, as it was nearly midnight!
So : you don't appear to have moved on yet, but I have done some research on DD behalf.
It occurred to me as I left you last night, besides the Baritone horn, there is also the Tenor horn, which is similar but smaller. And there is the Flugel horn, which is used in jazz, and some orchestras; it is similar to Trumpet but more mellow.
What is forming her choice, and when you say she has 'tried several instruments' I assume you mean just had a blow to compare the different sounds. Or do you mean she has learnt several instruments for short periods of time?
Whichever instrument she chooses, it surely needs to be one she can play in a variety of different ensembles, and as she gets older, the social aspect of playing with other people becomes increasingly important.
Our DS played piano, keyboard and recorder at primary school. Aged ten he was told he was too young for saxophone, so settled for trombone for a while. Then we learnt that sax WAS available to him, and he went on to play alto with his secondary school jazz band, and the county jazz orchestra.
If she wants to take music as a GCSE subject, when the time comes, piano or keyboard is also an advantage, as it helps with understanding Theory.
This is an excellent Brass feature by Durham County, and shows most of the instruments available: musicservice.durhamlea.org.uk/brass/
We used this dealer for DS sax, and they specialise in educational sales. If you can purchase through her school, you should get a discount and probably not pay VAT. When she goes to secondary school there may be more opportunity for music, and it is sometimes possible to hire instruments for lessons taken through school:
www.johnpacker.co.uk/Catalogue/Brass#.U0whu_iVv3A
I hope she enjoys her chosen instrument, and makes good progress.