You don't need a lot of fancy equipment or gear to get a great home workout. Indeed, you don't need any gear at all beyond your own body weight for many exercises and routines! However, investing in a few simple fitness items will help you get the most out of your home workout. These are all small items that will store easily in your closet or work-out area for handy use at any time. Considering a single month's gym membership can cost you anywhere from $20 to $50/month these days, you can purchase most of this equipment for your home use any time for perhaps the cost of just several months at a fitness center.
I've listed the items below in what I consider their order of priority - so even if you don't want to purchase all your home workout gear at once, you can get started with a few things quickly and get exercising as soon as possible. I've also included some sample home workouts on YouTube which illustrate how you use these various pieces of home workout gear.