If you were to pick one item to have in your Garage Gym it would be a jump rope. This is one of the cheapest pieces of equipment but can give you a great cardio workout. Whether your knocking out consecutive double unders or just starting with singles you will need to get a good jump rope.
A thin yoga mat can be used for situps or pushups and also protect your jump rope from wearing out when your practicing your double unders. The yoga mat works great to use for foam rolling at the end of a workout
A pull up bar is a good addition. Not only can you work on pull ups, but also toe to bars, knee to elbows, and hang and set of rings once you get them.
Next on the list is a set of gym rings. You can do ring dips and also pushups. If your more advanced you can bust out the muscle ups. Intermediate to beginners can work on ring rows and pull ups.
A plyo box would be next on the list and is a great tool for building your fast twitch muscles for jumping and hip power. These boxes are light weight and can be moved around the gym easily and are very versatile (jump over them and use for box squats.)
An ab mat is a great tool to compliment your situp workout routines. The ab mat fits under your back in the lumbar curve and is a nice addition.
Kettlebells are great for building hip power and endurance. Get a 35 lb kettlebell for starters as this may be the most versatile weight. Over time you can add and fill in the other weights as needed.
A barbell is a great item to have in your garage. Load up the bar with a few bumper plates and your good to go on shoulder presses, push press or power cleans. Finish out the barbell with a set of clamps to hold the bumpers in place. The spring clamps can get beat up sitting around the gym so find an old milk crate to keep them out of harms way.
Yoga mats are essential for doing ab workouts or stretching or laying around after workouts. These mats are relatively cheap and can be easily cleaned with some soap and water or just sprayed down.
Later on you may want to spring for a timer that you put on the wall but can get by in a pinch with your watch or phone.
Take your time and build your garage gym up as you need and pretty soon you will have all of your neighbors joining in for Saturday workouts with you.