Wow, thanks a lot for the really long and informative answer, Neko! This is a lot of information that I will be sure to keep at hand.
I actually just want a flesh piercing for now, not cartilage.
I am in Baden-Württemberg right now and several more times over the next two months. Very good cities for me to get the piercing done would be Mannheim, Ludwigshafen, Heidelberg, and I could probably also reach Frankfurt and Karlsruhe. When I'm with my parents, Hamburg is really good - this might actually be the easiest overall. Maybe you know anyone good in any of these?
I just remembered earlier that a friend had a tattoo done in the same city where I am now and she chose the shop really carefully. Do you think if they do tatoos properly, they'll be ok with piercings, too? Or are those too different to say that? Anyway, I might have a look at that shop.
Now, about the piercing touching other stuff - I guess you can just not sleep on the side the piercing is on, right? I should consider that when choosing the side...
And I should make sure to do it a while before my volleyball season starts again - even though the first piercing is probably rather small, being near a volleyball net with anything that could become entangled in it is probably not a good idea. I know people who cover their (healed) piercings with tape if they don't want to take them out, but that's definitely not sterile.
Thanks for your answer, too, Barmymoo! Considering how worried I am about infections, I think I'll follow Neko's advice and do it in a real piercing studio with a needle. It will be a birthday + getting my master's degree present for myself, so it's ok if it's slightly more expensive.