I recommend the following items to anyone looking for the simplest way to start any program requiring resistance training. At some point you will want to probably upgrade but this is your bare bones starter:
Yoga Mat – $15-30:
Great for core work and obviously yoga, Pilates etc. Recommended especially if you are working out on a hard surface. Some are better than others. I have found the GAIM brand to be longer lasting than the kinds you can find for $10.
Shoes: You really just need something comfortable to start. After a while you may find you want to get a good cross trainer for explosive lateral moves.
That’s all you need to begin a program! Like any hobby, there are add-ons, upgrades, and all sorts of ways to trick out your home gym. All that matters is that this gets you moving in the right direction. Better yet it is equipment that will still be useful even if/when you upgrade equipment. Finally, all of this fits in nearly any space. I have made 10′ x 10′ rooms work just fine and even living rooms with the coffee table pushed out of the way work. Don’t worry about having everything perfect, don’t worry about having all of the equipment, just show up. Show up and give it everything you’ve got with what you have!