Having a gym in your own garage/basement has quite a few benefits:
Listen to whatever music you like
No waiting for others to be done with equipment (especially the guy curling in the squat rack)
No travel time
Free to use as much chalk as you want
Playing around and experimenting with new equipment that you made. Most gyms these days frown on members bringing their own equipment to the gym
Quite a few serious Powerlifters, Strongman competitors, Olympic lifters, and other strength training trainees workout in very modest garage gyms. Tommy Kono, a legend amongst Olympic Weightlifters, has on multiple occasions trained in basements where there wasn't much more than a barbell and some plates; occasionally even a roof that didn't allow for complete lockout in overhead lifts.
Where most people stop short in the decision to make their own gym is the pricing, thinking it would take close to a $1,000 to supply enough equipment for their workouts. However a modest garage gym can be built very cheaply. Also that fee that you no longer have to pay for a membership can be used to slowly acquire new equipment, but for this article I will only be discussing the basics. Please note that this gym is for serious strength training trainees/athletes not someone who goes to the gym to do elliptical work.
The Core Basics
#1 is the good old fashion barbell the most basic piece of equipment and most expensive on our list. These days a brand new one will cost you about $300 as a set. However a used barbell is still a barbell and having a band new one or a used one isn't going to make your workouts any different. Shopping around Craigslist for a few weeks you should be able to find a set for $100-$150. I've heard of a few lucky souls getting a $50 bargain but that would be rare.
#2 Pull-up bar. No reason to get fancy here, a door way mounted pull-up bar will cost between $15-$25. I have mine that I bought 10 years ago for $10 and it still looks good as new. The only thing I had to replace are the screws that have been stripped over the years from moving.
#3 Saw-horses. Wait what? Instead of spending money on an expensive power-rack right away, two saw-horses will do just fine. I got this idea from Dan John, a strength coach from Utah and a contributor to T-Nation, if you are unfamiliar with Dan John's work I would highly recommend changing that. The added benefit, for the sadistic at heart, of the saw-horses is that to unrack the bar you have to do a dead stop squat since the saw-horses will set the bar at about waist level for most. A very basic pair of saw-horses will cost about $40 and they are good for up to 500 lbs. I wouldn't recommend spending more than that on the saw-horses because at about $100 you can start looking for Craigslist deal on a power-rack.
#4 Dip-belt. A good quality dip belt, like the one from Ironmind, will cost you about $60 and if you are using anything over 100 lbs it is absolutely worth getting. However for anything below 100 lbs a Home Depot belt with a carabiner and a chain will do just fine. It will work with loads above 100lbs but you'll be getting closer to the limits of the belt and taking a chance of it breaking. The belt, chain and carabiner will cost about $18.
This basic garage gym will cost between $260-$300 and allow for the performance of most of the basic exercises.