I was brought in for a custom home gym. The home owners were interested in what could be done for a low budget that would allow them to get a full workout. First I cleaned out the section where the gym would be. I inventoried the equipment they already had, met with them to determine their goals, and then determined what we needed to buy. They had a set of TRX straps and the ceiling mount for it. They had both types of punching bags. They had a weight bench and weights up to 35 lbs (with the interchangeable style of dumbbells). I suggested a tower for pull ups, dips, and leg lifts. They were also interested in a hyper extension bench and a durable mat for the floor.
Total cost for putting together the gym was less than $400. Depending on your goals you may or may not be able to make an affordable home gym. Getting stronger requires the use of progressive intensity. This intensity is hard to get with a limited supply of weight. For some exercises you can keep adding weight onto yourself, such as pull ups and dips, other exercises will be difficult to increase such as squats which will require far more weight than you can probably scrounge up.