Hanging doesn't aim to cause "choking", but rather to block oxygenated blood supply to the brain by constricting the carotid arteries.
If you do the procedure correctly, you lose consciousness in a few seconds, followed by death. Time, gravity, and your weight closing the ligature and the rope penetrating your neck will do the trick.
Breaking your neck only works for the Drop Hanging method (used in executions). And here you have more chances of making a mess, as you need to calculate the height of the fall, your weight, etc. We're not trained military personnel. It's also not easy to find a suitable location for it.
To start getting informed it would be better if you read these threads first:

Thread 'Evelyn's complete guide on how to hang yourself with both partial and full suspension hanging'
Are you new to hanging? Or maybe just trying to find out if hanging is the right method for you? This reading guide has you covered! This is your one stop shop to both partial suspension hanging and full suspension hanging. This is a reading guide to the guides I published on this forum so far...
sanctioned-suicide.net

'How to locate the carotid arteries?'
It seems to be said that I should be able to feel a pulse where they are but I can't feel anything . Any tips ?
sanctioned-suicide.net

Thread 'Do you need to find the sweet spot with full hanging?'
Do you need to find the sweet spot with full hanging? How reliable is it? How long does it take to get unconscious? How painful is it? How does it feel like while hanged? What is the difference between full hanging and partial hanging? Is there any resources here on this site regarding this...
sanctioned-suicide.net