I personally do more dumbbell chest press more than pushups or bench press. Why? Because this is easier on my shoulders. I think it is always better to have options for the training. One works good for me doesn’t mean works for you. You want to find out what works best for you.
Bench press vs Dumbbell chest press
There is nothing like one is better than the other. Both can target pectoralis major, triceps brachii and anterior deltoid. However, you can change the shoulder angle easily by performing dumbbell chest presses that may be easy on someone with shoulder pain.
Shoulder angle
Two images show different angles of chest press. If you “only” think about pectoralis muscles (chest muscles), 90 angle one may be better since weight that you are bearing is the further than the one at 45 degree. However, at 90 degree, the shoulders are not favorable and may impinge its joint. I would go with 45 angle one for the long term training.
How low should you go?
It depends on you. Some say the bar has to touch their chest while bench pressing. But if you have relatively longer arms, you may want to consider not bringing the arms too low (don’t pass the line of you back). Someone with shorter arms has more advantage of lifting heavy. No point to compare you to them.
Solution
Performing dumbbell chest press on the ground won’t let your arms go too low. I do sometimes when all benched are occupied. They are still targeting the chest, triceps muscles anyway.
Lifting lower back?
You may find you could lift heavier this way. But again in the long run, this is not good for the low back health at all. Keep the core muscles tight and the spine neutral all the time.
Learn the proper spine position by plank