Hi. I'm 23 and am really just starting to work out. I'm a smaller guy (5'9'' 145lbs) and I have a plan which I need some guidance on.
First, it's probably best to say that I would like to gain around 10-15lbs of muscle and simply be healthy.
Now, my plan which I need help with is as follows. Three to four times a week I'm doing as many push-ups, sit-ups, pull-ups and slowly lifting 16lb weights doing a routine called 21's (three different reps of 7 in a row) as I can. In addition to this I'm also doing a warm-up run and cool-down run, using a protein drink twice a day, and eating more good food.
If I continue doing this routine for the next few months will I see a difference? Will I gain weight?
Any help/ideas are be appreciated!
Oh, I am also going to join a gym in 2-3 months, I just need to develope a routine of exercising first.

Add some kind of leg work, even if it's only using body weight. It will add to overall muscle mass and production of growth hormones which will help you gain muscle all over in the long run. Since you won't be in a gym for 2-3 months, you will probably want to find some different variations or your body will adapt to pushups and pullups and you won't see further muscle gain. Add in dips, use water jugs or cans or bricks as weights, put your feet up on the bed to do pushups etc...

Ok. So I guess your answer was a yes, plus, add this and that. Is there a good website I can go to that will illustrate the variations on push-ups? I know that you work different zones depending on where your arms are but I'm having a hard time finding info about this.
What do you think about the 21's? Will this actually build my arms if I do 3 sets of these every other day?

21's are awesome, especially since you only have one weight (I'm guessing, since that's all you mentioned). You should see muscle growth fairly quickly, but since you're just starting, you'll see muscle no matter what you do. You might outgrow 16 lbs. rather quickly though. So, again, look for variation. If you change it up every couple weeks, you shouldn't see a plateau. Also, do not neglect the triceps. For one, you need to maintain strength balance, and two, visual symmetry.
We're not allowed to post other websites here, but google for "muscle exercise" and you should get some good hits.