This is going to depend on several different factors, your individual lever lengths (short torso/long legs, long torso/short legs, etc.), the federation and gear you plan to compete in (ipf, wpo, etc.), and also what feels most comfortable to you individually. In IPF singly ply gear, it is going to be on average more advantageous to use a narrower (shoulder width or slightly wider) stance, and you will need more depth as well. In a canvas suit it is by far more advantageous to use a much wider stance, sit back into the suit, as the canvas suit "catches" the lifter at the bottom where the polyester/ipf style suit provides "rebound" out of the hole.
As far as training goes, alot of the wide stance canvas suit style lifters train in squat briefs or power pants, and use a slightly more narrow stance than they compete with, the briefs will save the hips during training but not provide the nearly the same degree of assistance as the suit does, and allow training with more modest weights. Squatting with the straps down is also a viable option. I am assuming you are planning on using gear due to your goals, so the width of your stance when training will need to accomodate your competition needs.
Definitely take it slow if you have an existing lower back injury, I didnt see exactly what that injury was and you could definitely have some technical issues or be doing excessive lower back work and not enough glute work at the moment. Reverse hypers are a great exercise, but lifters can easily be making them into a lower back dominant movment instead of leading with the glutes and hamstrings. The strap attachment will generally give a little more glute/ham involvement while the roller attachment will tend to involve the lower back a little more. good luck with your training and hope your injury heals quickly.