I have two kids at Newton British School and we are very happy there. The fee is really reasonable compared with Campass which is so expenssive for I don't know what!! Their building is cheap and their teaching could be matched by many lower priced schools! There are many good schools and many bad ones too. I don't know about Choueifat but I know that it is much more reasonably priced compared with Campass. I also heard that their teaching is solid even if it is a bit old fashioned.
Go and see Newton in Alwaab area. I also know that Newton is opening a new campus in West Bay. Here is the website for Newton schools:
www.newtoninternationalschool.edu.qa