Hello Marc, I'm pretty new to this myself (having read MCTB last week), but I believe I got to first jhana yesterday (pretty excited!) and I can say what worked for me.
Definitely focus on the actual breath, not on counting. You're concentrating on actual physical sensations that accompany the breath. Try to stay with them without any breaks. It's okay to be distracted by noises or thoughts as long as you also stay with the breath at the same time. It's like driving a car - you can experience things not related to driving, as long as you're focused enough not to crash. Not staying with the breath is a kind of crash

You should gradually notice that the physical sensations accompanying the breath are actually quite complex and there's enough going on there to sustain your concentration. Try to keep track of all the details of the sensations - it requires more concentration and in-the-moment presence than just counting breaths. You don't need to label them or think about them (just like when driving, you don't have to think "car, car"), just be aware of them. Provided you make an effort to keep track of all the sensations, you will have less and less room for being distracted, and more interest in following the breath.
Eventually you should have a pretty detailed, quite stable (provided you keep concentrating) "mental model" of your breath as it changes instant to instant.