To begin this look at fundamentals, the first topic is posture and playing position, which are related.
Keep it simple
The simple answer is to hold the horn in a manner where your body is in the most similar position to a normal standing position, and maintain that basic setup when seated. The positions seen below are from my Introducing the Horn book, and would serve any player well.
What about playing on the leg?
I’m all for being comfortable, and if you are a new and especially if you are a young hornist, you may feel the need to adopt a playing position that is on the leg. Which is fine, I played that way for years.
But if you are too tall to play on the leg, your posture can get kind of wonky, as seen in this illustration.
The very young hornist
The very young hornist will have to work out their own compromise, the illustration below being among the options.
The right hand
The main thing I come back to students about over and over is that over time your playing position and posture needs to be reevaluated. That includes overall posture and the general right-hand position. This final illustration shows a couple generic right-hand positions — which are actually the same position, but rotated around the bell. The one on the bottom is for playing with the bell off the leg and the one on the top is a traditional option for playing on the leg.
We will talk more about the right hand when we get to the topic of stopped horn.
BONUS: Additional concerns RE: imbalances
A final posture point should be mentioned primarily in relation to adult players. What happens is your overall posture (!) will be influenced by your horn playing, as the horn playing has caused imbalances in your body.
In my own personal case, my shoulders are shifted slightly to the left relative to my hips, and I certainly overarch my back. Not to mention that my left arm/shoulder is much stronger than the right, etc. Working with a physical therapist in recent years has been helpful.
I think body imbalance issues are almost inevitable for the aging hornist. Which also speaks to if you can set up with good posture as a new hornist it will help avoid problems later.
When the series continues the topic is fingering.