It's really hard to diagnose something like that over the internet. We all have widely varying embouchures. One person may need to have their placement be really low (very little upper lip in the mouthpiece like Kai Winding or trombone shorty) or very high (the opposite, like Joe Alessi), or off center vertically... or it could be fairly centered (like Marshall Gilkes). And then the direction and the method of motion differs from person to person as well.
There are several schools of thought on this, the big pedagogues that a lot of brass playing stem from are Remington, Reinhardt, Caruso, Farkas, and Jacobs, among others. Some seem to work well for certain players, but seem to not work at all for others. I was taught by a lot of Remington players for a long time, and it wasn't until I started studying with a Reinhardt style teacher (Doug Elliott) that my playing began to take off.
In my particular circumstance, the way that I set to play the Bb an octave above written treble Bb is optimal for my embouchure, and so when I warm up, that's the first note I play and I bring that set down with as little motion as possible. When you do it right, there's actually very little in the way of strain because high playing. For others, starting somewhere closer to the center or bottom and bringing that set up or outward to minimize motion is ideal. Again, diagnosis is impossible without seeing someone.
In the Caruso camp, the very, very general idea is to not think about what you're doing, but to focus on letting your body figure it out. Sam Burtis has a great book available on exercises you can do to figure out where you need to go to make your particular equipment work. One of the key beginning exercises is to play multiple octave scales without removing the mouthpiece from your lips. At all. Even to breathe. You breathe through your nose and do not remove any part of the rim from your lips. This minimizes motion and forces you into a set that works for the range you are working with. I find that works very well for a lot of my students.
As far as for if buzzing is good or bad... there are a lot of opinions about this. It seems like a lot of Remington and Jacobs teachers swear by it whereas Reinhardt guys find it to be borderline useless. I know Doug Elliott only recommends freebuzzing that's done properly. His idea of properly is never below middle F (4th line bass clef) However, it's quite an exercise in futility explaining how to properly freebuzz over text. If you want to pursue freebuzzing, I'd highly recommend contacting someone who is in the Reinhardt camp like Doug Elliott or Dave Wilkins.
That said, one useful exercise that may help your situation is to play a pitch on the instrument and then remove the mouthpiece while you are still playing that pitch. Hold the pitch constant throughout the procedure. Then do the opposite. Buzz a pitch into the mouthpiece while inserting it into the horn, again keeping a consistent pitch.