I can say I have a lot of experience with braces and teeth being pulled. My teeth were seriously messed up and they had to do a lot of work to make them look the way they are now.
They started very early with me, I think I was about 9 years old and they had to pull a lot of teeth. I had 8 babyteeth and 4 normal removed, to make room for the new ones since my jaws are quite small.
They say that removing babyteeth is a lot less difficult, but mine still had all of the roots, so it wasn't any different from normal teeth...
They don't "knock you out" here in the Netherlands, unless you go to special dentists, they just numb your jaws.
Having your teeth pulled isn't a very pleasant experience, but I think the needles are the worst, they seriously hurt. After that has been taken care of it's just a weird experience, all the pulling and all, you can hear crunching and stuff. They didn't stitch me most of the times, I just had to bite down on bandages for a few hours.
I never had any wisdom teeth removed, my sister has. One piece of advice: put ice on it as soon as you can! It definately helps to reduce swelling and pain. Sometimes they say it isn't necesary, but I can tell it really makes a difference.
As for the braces, it doesn't hurt when they put them on. It only hurts afterwards, when you feel the pressure on your teeth. It depends on how much your teeth have to be corrected though, when it's only a small bit they can take it slow and don't put that much pressure on them, so that it doesn't hurt that much. I would advice to take pain killers a few days after and eat soup and other soft things as it can really hurt when you bite down on something.
After a few days the pain should be gone and you won't notice the braces, you get used to it. When I had my braces removed it felt really weird to have a smooth surface again
My teeth were very "stubborn" and after about two years after I had my braces removed, they were already messed up again. It was not as bad as the first time, but I chose to take braces again (I was 14 years old then). After they removed those they glued a small steel wire behind my teeth to prevent them from moving again. The wire broke off after a few years, but now I can say my teeth finally have a fixed position. I still have an overbite, but my teeth are in line an I don't feel like having an operation to correct the overbite, as it cannot be corrected by braces anymore.
I'm happy I went through all of this though, as it looks a lot better. It isn't always a pleasant experience, but it does pay off in the end.