I am a center player. In fact, I even play tenor in the center. It is easier and more comfortable getting the mpc to the correct position and angle.
With that said, smaller students I start on the side. The determining factor is when they can play the lower stack without resting their wrist/hand on their leg (or distort the arm to get low enough). Those that need to start on the side to do this move to the center when they get tall enough. If they have to start on the side I am fanatical about being sure the neck/mpc is set up to bring the horn to them - not go to the horn, ESPECIALLY leaning over sideways! This may be limited by the construction of the octave key as if you turn the neck to far it can force the key open. In that case, turn the lower body slightly in the chair to get the horn closer to the center.
Last is the biggest issue with the neck strap - and I will say I used to do this too, which is why I know about it. Be sure that after putting on the strap they return their head/neck to the natural and upright position. The tendency is to bend down to put the strap on then never get out of that hunched position. Best way is to teach them to put the strap on without bending down to it (it isn't really heavy...)