When wanting to set up a home gym, all you really need is a space, i.e. a separate room dedicated to the purpose, a few weight benches and a few dumbbells. You do not need the latest and greatest, most expensive equipment out there and with said equipment you can make a good start and build from there. A weight bench is nothing but a sturdy 3 foot plus long, 1 foot wide padded bench that will form the bases for your workout equipment. Some can be adjusted to be elevated and will set you back less than $100 new and even less second hand.
With your imagination you can use two benches to thoroughly train a number of muscle groups from pectorals (chest), triceps (back of the arm) and deltoids (shoulders). If you add a few dumbbells you can add the biceps, forearm muscles and even legs with exercises such as dumbbell squats to your repertoire.
An example of using your benches to exercise the pectorals is the high intensity pushup. You align the benches about two to three feet apart, parallel to each other and assume the pushup position on top of them, one hand on each bench. You then can go down as far as you can before you push back up. You can start with your feet on the floor and later place them on a third bench increasing the effectiveness of the exercise. Another exercise example is the back hand dip between the two benches for the triceps.
As you continually can afford it you can add a couple of bench press racks that can go either side of a bench and some barbells. If you want to expand your choices even further you can add some even more specialized gym benches such as preacher curl benches or Olympic multi benches.
The point is that you can start off with a simple utility flat weight bench and as your knowledge increases and consequently your need to specialize further you can acquire the more specialized equipment. Who knows where you could go from there because if you put together a nicely equipped home gym, maybe you could start charging people in your neighborhood to use it if they so wish. Thus you can create a nice little income on the side as well.