What You'll Need Buy:
A sturdy padded workout bench. Don't buy a cheap one because it will eventually break. A bench with solid legs and a nice padded bench will run you $100-$200. If you want to get really cheap head on over to Home Depot and get a wooden bench. I used one from Home Depot for over year. Cost me $30 and I just covered it with a couple towels and a yoga mat for extra padding.
A small variety of free weights. You don't need to buy every weight in barbells. Depending on how much you lift 4-6 barbells should be sufficient for at least a while. For example I have two 25lbs barbells, two 30lbs barbells and one 50lbs barbell.
A curl bar with a small variety of weights for increased and decreased difficulty.
TOTAL FOR AT HOME GYM: $300
What You Don't Need to Buy:
You don't need to buy push-ups. Push-ups are free. You don't need to buy sit-ups. Sit-ups are free. You don't need to buy a chin-up bar (though it is nice to have one). Instead, find a park with some monkey bars or an adult parcourse to do chin-ups and pull-ups.
What You'll Need to Do:
Like I said before, this won't be easy. You'll need to be dedicated. You'll need to do research about different exercise you can do with the equipment you have. You'll have to be able to disengage yourself from your home life. That means no phone, no computer, no TV. Get your workout on, forget the other stuff. It's tough to not get distracted at home, but with a little practice you can do it.
What You'll Need to Do, but Probably Won't Want To:
In order to get into fabulous shape without going to the gym you'll need to run, run, run, and then run some more. Running will not only make your heart and lungs stronger, but it will burn the fat off your body and allow for all that muscle mass you're trying to increase to show up on your body.
A Gym Member$hip:
Even if a gym membership is a fairly low $20/month you will still be paying upward to $240-$500 a year for a gym membership. Not to forget you will also be paying for the gas that you use to get to and from the gym. Needless to say, in the long run, if you can develop a solid at home workout routine, supplemented with plenty of running and some creative thinking you can and will get in fabulous shape without going to the gym.