Here's some ideas for equipment that I consider a good investment for a small home gym set up:
A set of Dumbbells: You can do pretty much any move imaginable with a set of dumbbells, including all moves designed for the barbell. Just hold two dumbbells even with each other like you would if gripping a barbell and go for it, with the same form and move. An even more cost effective way to invest here is to find a set of adjustable dumbbells that adjust as low as 5lbs and as high as 100 lbs. You'll save a lot of room too. I chose to get a proper set of regular dumbbells because I like to do supersets and find adjusting and readjusting to be a pain in the butt. Pick what's right for you.
Fitness Bands: These make pretty much any cable move you'd do in a gym possible at home. Just make sure you also purchase a door anchor for each weight fitness band you buy (because switching out your door anchor from band to band depending on your exercise is also a pain in the butt). Fitness bands can be used to do weighted squats, bicep curls and other various exercises. With a door anchor you can also use your fitness bands to do Lat Pulls, Cable Rows, Cable Crunches, Presses, cable tricep extensions... the list is limited only by your imagination. If you're not sure what other exercises you can do, invest in one of those small pamphlets that outlines all the exercises ... or head to YouTube and start watching videos.
Fitness Ball: if you don't have room for a big ball rolling around your home consider removing one chair and using it as a chair when you aren't exercising with it. These are great for core strengthening and can also double as a bench for some exercises such as bench press and flyes.
Jump Rope: a great way to get some cardio without leaving your livingroom!! Just make sure you move any furniture or breakables well out of the way first. But you really don't need more than about 5 square feet and a 8 foot ceiling to jump rope in your home. That's all I have.
A Pull-up Bar. Well worth the investment. If you think you can't do pull-ups, you're maybe right, but the road to being able to starts with one attempt. It doesn't take long to be able to do just ONE. Two comes VERY fast after that, and soon you'll be doing them and bragging to all your friends how many you can do.
There you go. Some minor investment in these pieces of home equipment will not only save you hundreds of dollars on gym fees but will also give you the ability to do well-rounded workouts right in your own home, regardless of how small your space is.