There are a couple of ways you can work up to doing push/press-ups.
1) Knee push-ups. I think this is what you meant as "crawling position" in your post, but I'll put this in anyway. This is where you use your knees as the fulcrum instead of your feet in order to reduce the resistance. Make sure your back is straight & stabilized. Here's a pic of the top position:
http://www.strength-training-woman.c...-Push-Up-1.jpg
2) Do the negative ONLY, e.g. start in the 'top' push-up position with your arms extended (but not locked) and your back as straight as a board. Then just slowly lower your chest to the ground. Repeat this until you've built enough chest and shoulder strength to then push chests up from the floor.
As varbo said, push-ups are primarily chest oriented. For your arms, there are a number of exercises:
Bench Dips (triceps):
Weighted Bench Dip
Pushdowns (triceps):
Cable Pushdown
Hammer curl (forearms):
Dumbbell Hammer Curl
Dumbbell curl (biceps):
Dumbbell Curl
Pull-ups/chin-ups are also a great way to get your forearms and biceps simultaneously. If you can't do a complete pull-up, then try doing the negative only --> hanging from the top position and slowly lowering yourself downward. If you have access to an assisted pull-up machine, that would be even better.
Note: Don't confuse the differences between the Hammer Curl and the Dumbbell Biceps Curl.
Once you start developing a baseline standard for your body (being able to do a number of push-ups, etc), then you'll be able to do even more bodyweight exercises that are capable of working multiple muscles at once! For example, pull-ups (aka chins) are primarily for the back (lats) but also are great for working forearms and biceps.