Hi Alex,
You will get stronger and firmer muscles over time using your push up workout, but to be honest, if you want my advice, get back on the bench press, however change your technique slightly.
Now I will warn you now, do not be disheartened if you have to actually DROP your weight slightly here, because I guarantee you, your strength gain will increase alot faster than it has ever done before.
On the bench press, your goal is to perform 8-10 reps, using a weight where on the 8-10th rep you are really struggling. Struggling to the point that every time you do the exercise, you need a spotter to help you with the last rep, or be there as you push yourself to failure. You MUST push yourself to failure.
Now here is the key. You must work your muscles working time under tension (TUT). The way you are going to work out is using a ratio of 2:2:2. In other words, from the start position, with your arms straight, lower the bar making the movement last a full 2 seconds, then hold just above your chest for a full 2 seconds (I bet you weren’t holding before), then push up making the upward phase last a full 2 seconds, then go straight into the next repetition. Like I say, do not be put off if you have to lower the weight slightly.
If you want to train for hypertrophy (building muscle), make the release phase - that’s the downward motion - last 4 seconds instead of 2 seconds.
A slightly better option thou than the bench press would be to do the Dumbell Chest Press. This allows you to work each side of your chest individually, so both sides of your body have to do the same workload. With the barbell, the weight is spread across the bar, so one side may be doing slightly more work than the other side. Also the Dumbell Chest Press is safer too. You can push yourself to failure without the essential need for a spotter. If you run into trouble, you can just drop the weights down either side of you. Run into trouble with the barbell, and your pinned to the bench, which can be very dangerous (not to mention rather embarrassing).
So, bottom line, time under tension. Try it, and just feel the difference in your workout straight away.
Good luck, and let me know if you need any help.
Ben :)