pushups and bench are a similar motion, they will help each other..BUT pushuops use a lot more core muscles, as mentioned they are a great exercise.. Most people fail on the core factor rather than the chest tricep strength when starting them.
I would do what ever is heaviest first, or what ever you get the best range of motion from.
Ie bench, then push ups, then knee pushups, then I would try and do plank holds, for aslong as possible, a solid core will help heaps for push ups,