Hi Sophie, with orchid growing, you will find out later, we all have different approaches to it. Looking at your plant, it does need a repot, into a container with drain holes and if you can, make side holes too. Phal roots are always like that, grows out anywhere it likes. I have learned to tolerate it, since in its preferred environment, that is the way it attaches to limbs of trees. Those roots also do some photosynthetic process, which helps the plant too, so at times I just let aerial roots wander about, if it wants too. It grows such thick roots, and loves very good airflow around it.
I do not cut off healthy roots, what I do cut off when I repot are the obviously brittle and dead roots, if there is any. I also inspect the underside of the plant, and I try to remove gently the old media. Gently wet the live roots, so it becomes more pliable to handle, that way you can gently put it in whatever container you will use. You will also find out that orchid growers use different media for their orchids. But for starters, I would get chunky orchid bark mix, and before I repot, I soak them in water overnight, to open up that dry bark, then the following day I toss away the excess water and use that for the repot. It is a bit daunting to do the repot, but we all have to start somewhere.
So first things first, prepare your media and container, once you are ready then proceed to do your repot. Also when I repot, I try to tilt the plant a bit, so during watering time, excess water flows away from the crown. Do not bury the collar of the plant too deep, just bury the roots if you can. Later on if the roots wander out, you can again gently wet it, and carefully put it back into the container, or just let it be. In time you will find out what media works for your area. We all have our preferences. I have learned not to use sphagnum moss, since it is hard for me to determine if it is dry enough. Our growing environments are different, so be observant of your temps and humidity levels. Position your plant away from direct sun. It is a low light plant, that is why it is so much fun to grow indoors and when it blooms, it can last for 3 to 6 months.