I am not saying I am not willing to do it, I just donāt want that to be the start.
If you have a good teacher then you won't get into sparring until you have some base skills to work with. Some people get into sparring faster because of previous knowledge. For example, it took me 2 years to get 2 female students to spar. The biggest challenge for them was the "fear of sparring" in their minds they thought they were going to get hit hard like some of the other students. It was really difficult for them to believe that students lower the skill level to match the opponent as needed.
Once they got into sparring they loved it and would request it more than the guys who generally had to take a week or two for healing after being bruised from regular training and sparring. The women were bruised too, but not to the same extent. Everyone that I've train in sparring often smiles during sparring. If your teacher is good then he or she will introduce sparring to you in the right way.
but the main focus would not be punching someone,
For martial arts with striking, this will always be your focus even when you aren't hitting someone. When I do my forms I throw punches as if I was hitting someone. i get the image in my mind to help me visualize how I should drive the energy for my punches and how I should target them. None of this is important if you don't plan on using martial arts for self-defense. If you plan on using it then striking the target and visualizing a human target is greatly beneficial. That's just the nature of martial arts application. There is a difference between focusing on punching someone and actually doing it. I've been doing martial arts on and off since I was 8 years old. I've always focused on punching someone. My last street fight was a long time ago maybe in my 20's or before then. I'm 46 years old and when I train train forms, I focus on I focus on punching someone in the jaw in a way that affects the neck. When I spar I focus one punching someone in a way that allows me to learn my techniques and keep my sparring partner fairly safe. They still get hit but I don't blast them.
Remember. Keep in mind that you stated you want to use martial arts for defense so it's just part of what you have to do. Hit with a purpose, kick with a purpose, train with a purpose. Just throwing air punches without a purpose will keep you feet but will be detrimental to your ability to actually use it. The things I'm telling now are the things I would tell you if you were my student.
being thrown on a matress and all that
Unfortunately you will have to visit this at some point. It happens and those who don't train it usually end up on the ground in a real fight with someone on top beating the snot out of them. If you want to protect yourself from someone taking you to the ground and beating you, then this is part of the training.
If I was interested in the fighting I would go for kickboxing or any of these punch and throw stuff, which I am not attracted to.
And this is why I recommended that you take martial arts for fun and then take self-defense classes so you can learn how to avoid trouble vs fighting your way out of trouble.
hat is why I have oriented myself to another kind of style, that to me, at least from reading about it, would not offer what you are saying in the start.
Any respectable martial arts teacher would not throw you into sparring or attacking right away. First you have to learn the basics, such as how to throw a proper punch with correct structure. How to cover from hits. You would first be thought the correct way to do things, which protects you from hurting yourself. I've seen more hurt themselves from throwing incorrect punches than from sparring. I had a bunch of videos related to this but I can't post them because of the rules of Martial Talk. Just know that people hurt themselves all the time by punching and that's because of poor punching structure. A good teacher will make sure you get that correct first.