21 Africa Safari is a very good tour operator
I booked a group tour for climbing Mount Kilimanjaro via Lemosho Route. However, in the end I was alone and had a private Tour. Nevertheless, it was a great experience and I got to know other climbers so I wasn't really alone/lonely. A private Tour also has advantages because you can do breaks whenever you want to, go your own pace etc. without having to take care of other group members. Elieth was very helpful in planning and answered all my questions within a few minutes.