A few points:
When doing pushups (or pull-ups, or sit-ups), the most important thing is to do them PROPERLY. Back straight, touch your chest to the ground and recover to where your arms are fully extended. Doing a couple of proper pushups is much more beneficial than doing 25 when you are "cheating." A proper pushup tones arms, legs, and "core."
If you can only do a couple, it is good to work with a set of stairs. Pick a stair (maybe the second, third, or fourth) on which you can do at least 10 proper repetitions. Do at least three sets over the the course of 10 minutes. When you can do that easily, move down a step to the next level. And so on.
The benefit of added repetitions beyond 15-20 is minimal, and places unnecessary strain on the wrists and elbows. Doing three or four sets of 25 provides basically all the benefit that can be had from doing pushups.
Pull-ups are a fantastic exercise, but for most people they are just too difficult to do a significant number. If you have access to a "Gravitron" machine or something else that allows you to do an "assisted" pull-up, it is worthwhile to use it. If not, you can gain significant benefit by doing "reverse" pull-ups or by simply holding yourself up from a pull-up bar. A "reverse" pull up is when you start at the top position (mounted from a chair or whatever), the lower yourself as slowly as possible to the fully-extended position. If you start with reverse pull-ups, you can build up to a single proper pull-up, then to multiples. 10-12 is optimal, because as with pushups, doing more reps places undue stress on elbows and can actually hurt you. Remember to alternate palms in and palms out, as they work different muscles.
Don't forget to include crunches and side crunches in your routine.
You can get a pretty good workout with no equipment at all.