Harry Berv has a number of thoughts on proper playing position in his classic book A Creative Approach to the French Horn. In this first quote he also notes a few words to live by if you played (as he did, with his brothers) in an orchestra conducted by Toscanini!
Sit in a relaxed, upright position. The right leg should be back and the left leg forward, with knees separated but not spaced too widely apart. The arms should be held loosely at the sides but not allowed to stick out at the elbows….
The body should be bent slightly forward in a ready, poised position. Avoid reclining against the back of the chair and perhaps being too relaxed—not keyed up enough or sufficiently alert to give what is being demanded of you. Being too comfortable and overconfident can be as detrimental as being overanxious. Your head should be at a slightly inclined position to minimize strain on the neck and shoulder muscles. If necessary, the mouthpipe can be raised (by a repairman) so that you need not bend your head down too far…. It is very disconcerting for a conductor to observe a player’s head buried behind a music stand, his eyes seemingly focused downward. It creates the impression that the performer is obvious to the directions being given from the podium regarding beats and nuances in the music. I recall an irate Toscanini at times reprimanding musicians who appeared to be “sleeping” on the job.
Berv suggests playing the horn on the leg but if this does not put your body into the correct position he has several suggestions.
In discussing good form, it is important to consider the significance of compensation. If you have short legs or arms, you can raise your right leg and bring the horn up closer by placing a block of wood or a book, the size of which varies according to individual need, under the right foot; this might also be helpful if you have a long torso, as you might otherwise tend to bring your head down too far to reach the mouthpiece.
As to left hand position Berv recommends that “The fingertip pads of the left hand should be placed evenly over the center top of each key to insure the comfortable manipulation of the valve levers and allow for maximum technical dexterity.” If the little-finger hook is not in a comfortable location it “can be adjusted by a skilled repairman to suit the size and shape of your left hand, thus helping avoid discomfort that might be caused by the hand being too cramped or spread too wide.”
Finally, as to playing standing Berv notes that
I do not recommend that you practice in the standing position, even though there may be occasions when you will use that position—in marching bands or while playing a solo, for example. The standing position puts unnecessary pressure on both arms. It is clearly less tiring to practice in the sitting position because it permits a more secure grip on the instrument as well as a feeling of total playing security.
As noted in in relation to prior quotes in this series, that is a bit “old school,” Berv was an on the leg player but playing off the leg is much more common today.