You can do pushups to warm up, just don't go crazy the day after you work chest. 48 hours to recover from soreness for the same muscle group. Although there was this guide called something like extreme muscle growth volume 2 or whatever I order and he was suggesting that the size of the muscle was more of a consideration on how long you needed rest. I don't remember exactly, but I think the implication was that you could work arms with less than 48 hours apart. There's an argument for everything, I work abs everytime I go to the gym but there are conflicting viewpoints that suggest you treat them like every other muscle and do low sets with weight. But really OP, it depends on what your trying to do.
You wants mass, you go for more rest, heavier weights and heavy eating. You want endurance/cardio in your lifting then do bench every day. I think Navy Seal prep. suggests you do pushups, pull-ups, sit ups and run every day with one day rest.