Also, push-ups may be easier than Bench press, but your body still needs time to recover.
Every other day is more than enough. Everyday is to much.
A good rule of thumb: if you are sore, don't workout that bodypart.
Now, in the long term, only doing pushups will lead to uneven develpoment. The antagonist to the pushup is the pull-up or row. Doing pullups as much as your push-ups will equalize your upper-body muscle develpoment. Just as the pushup works your chest, the pull-up works your lats. Push-up hits the triceps, pull-up hits the bicep, etc., etc.
For a beginner, those are the two most vital, compound exercises. And, they can be done at home w/ a pull-up bar and a clean floor for push-ups.
Add sit-ups/crunches and a running routine and you have a real basic but effective fitness regimine based off the military system.
-Good luck