I would suggest, keeping in mind the bad back, not doing overhead presses seated. It puts weight directly onto the spine and compresses it into your tail bone which is worse than standing. The legs, hips and arch of the back provide a buffer against this standing.

Seated incline bench presses on an incline bench would be better than any of the aforementioned overhead presses insofar as protecting the back is concerned as it minimizes the lower back involvement in the movement. The stress is placed mostly on the pectoralis minor and front deltoid.