Since I know a decent amount about fitness, I will help out
Considering your age, I would advise you to see a doctor prior to starting anything. Its better to be safe then sorry..
As far as exercises, I would suggest walking for at least 2 miles a day, for more rigorous exercise use an exercise bike. I wouldn't start running for a while, it can be very stressful if your not used to it. If you can do more then 6 push ups great, if not its ok. If you struggle with push ups, the bench press will help greatly. Pull ups are great, but many people aren't strong enough to do enough of them to really strengthen their muscles in any short period of time. Sit ups are ok if your form is proper, but there are better ways to hit the abs.
To give you an idea, in any given week I walk about 12 miles (soon to be 5 miles a day 6 days a week), I do 4 sets of bench presses, 4 sets of barbel curls, 4 sets of military presses, 5 sets of dips, 4 sets of squats, and other assorted exercises that change every week. I have been primarily focusing on upper body strength. I will be the first to admit that I have neglected my mid section quite a bit, but I am going to be focusing more on that in the upcoming weeks. Its really good to work your entire body, not just upper body.
To give you an idea of strength gains, I have been able to up my bench press by 10 pounds a month on average, 6 pounds on average for the curl, 6 pounds for the military press, 10 pounds for the squat, 2 extra dips a month, and so on. Realistically you should see at least half of that for gains, if you exercise properly/regularly and eat well. I could very well see greater gains, but my diet is not good by any means. Sleep is a must, its best if you can sleep for at least 8 hours every day that you hit the weights.
In the following weeks I am switching my entire workout routine, onto a track that will be focused on mostly strength. To train for strength its best to do low reps of heavy weights. Meaning rather then 12 reps of a certain weight like say 140 pounds, you do 6 reps of 170. Heavy sets are best for strength gains, however you form has to be perfect, or injuries will happen. For most people its best to start out with the higher rep sets of a lighter weight, it allows you to get your form right, and its easier on your body.
I prefer to work out with free weights, however the newer bowflex machines (and similar all-in-one gyms) offer many advantages. They take up less space, they are safer, they offer many exercises, etc. If you want to work out in your home, get a good bowflex to work with, its worth it. If your planning on going to a gym, then it wont be too big of a deal not having your own equipment.
One last thing I want to mention, its a good thing if you set realistic goals for yourself. In my case I really need to have something on paper that I work towards, otherwise I feel like I am not doing anything. In your case I would say these are realistic goals:
Bench press = at least 1 rep of your body weight
Curl = at least 1 rep of 55% of your body weight
military press = at least 1 rep 60% of your body weight
Squat = 1 rep of 80% of your body weight
Pull ups = At least 8 pull ups
I could go on for all the exercises known to man, but those will at least give you something to work with. Now I don't know how in shape you are right now, the realistic goals I mentioned might take you 3 months to hit, or 2 years. Only use them as an idea, set your own for yourself