The issue is that many people will argue that it's too tough to have a "home gym". They don't have enough space, or they can't afford big machines. The truth is that a home gym is what you make of it, and it can be so much more simple!
My own personal home gym is actually my living room. While in my undergrad, it consisted of a 3'x6' space between my bed and the wall where my yoga mat would fit. During my grad studies, it was my basement: a huge open space with a cold, tiled floor, and no furnishings. Just a makeshift table that my laptop sat on and oodles of basement space to do some kickboxing videos or animal flow.
Now, in my very own house, I transform my living room into a home gym. It's more affordable than you think and the only "set up" is moving the coffee table out of the way and rolling out my yoga mat:
1) Yoga (P90X yoga, a few Rodney Yee videos, and Wanderlust TV's 21 days of yoga which can be streamed online for about $30 for full access anytime you want)
2) Weight aerobics: I love The Firm and all of their videos but their original ones from the 90's are by far the best workouts I've ever done!
3) Cardio: Cardio-dance-kickboxing fun, I have a collection of Turbo Jam and Turbo Fire DVD's from BeachBody's Chalene Johnson. Totally fun, and I can still manage it in a small space.
Building your home gym
The above workouts are just a small tasting of what's out there. I highly recommend visiting www.collagevideo.com to checkout a variety of workout videos. See what you like - what looks like fun and what you would be interested in doing. Based on what which workouts you want to add to your collection, you can start thinking about the equipment you need.
In general, start with a yoga mat. Something for you to work on, or stretch on. Any mat will do, though I'm in love with "The Mat" from Lululemon as it provides extra grip support and doesn't slip.
If you want to include yoga, invest in yoga blocks. These by far are my favourite accessories. They can help with posture and support, even with just sitting on the ground.
Beyond that, work up slowly with anything. Always start a new workout without any weights at all. Just go through the motions and get used to the new routine. Then work up in weight. Start with 1-3lbs. In the picture above, I have a set of 1 lb hand weights (pink), 3lb dumbbells (black), 5lb dumbbells (green), 7lb dumbbells (silver and pink), and 2lb ankle weights that used to belong to my mom.
The nice thing is that you don't need to buy 3-5 sets of dumbbells all at the start. For most beginners I suggest picking one super light hand weight (1-2 lbs) and one slightly heavier dumbbell (3-5lbs), depending on your physical strength and condition. That's really all you need to start. For a lot of videos and workouts, you might not need any weights at all.
To make things even more affordable, focus solely on body-weight exercises, (or hook up a TRX system). These don't require any hand weights at all, just your own body and your own strength. The goal is to find a routine that you love to do. That way, exercise isn't a chore, it's a part of your daily body maintenance, a fun activity, and part of your everyday life.
