Hey Annabeleee,
I would recommend the TRX, it's a suspension training system, very affordable compared to other home gym system, yet much more affective in my mind. You basically need the TRX and a door attachement, and you're ready to go. I use it at the gym to add some diversity to my work out, and it's excelent for working out your core, as well as easy to adjust the intensity and quick to change from one exercise to the next. At first glance it doesn't look like much, but once you look up different exercise programs for the TRX, you realize how much you can actually do with it.
Furthermore, I would buy myself some kettlebells if you're serious about working out from home. for guys, the 35lbs and 45lbs kettlebells should do the trick, women would usually need a lighter one like a 20 or 25lbs kettlebell, as well as a 35lbs kettlebell. The only tricky thing with kettlebells is that you would have to buy a book on how to use them properly, which I would suggest "Enter the Kettlebell: Strength Secret of the Soviet Supermen" by Pavel Tsatsouline.
In case you're wondering why I'm suggesting these two systems, it's because you can burn more calories and get in much better shape simply by using bodyweight,suspension training, and kettlebell exercises than you could ever hope with any of those universal machines or bowflex garbage that they sell you for thousands more.
Although fairly technical, if you can learn the turkish get-up, Kettlebell swings, and kettlebell snatches, mixed in with some TRX workouts, you could be in the best shape of your life without leaving the comfort of your home. This type of equipment works great for super setting, and for interval training, which gets you the best workout in the least amount of time.
For the record, I'm only pormoting this because I know my stuff, not because I get anything out of you buying either one of these things. Also, if you rather buy another suspension training system, it would likely be just as effective as the TRX, I'm just not familiar with the other ones, and have experience with the TRX, so I'm mentioning that one.
Furthermore, if money is no object for you, and you want to go all out, then I'd say buy a BOSU Fitness ball, Medicine balls, and finally, if you're really hardcore, a squat rack, adjustible bench and some free weights, both barebell and dumbell weights. This would create a complete gym in your home, but most people don't have the money, space or interest to buy all these things. So, if money is an issue, then start with TRX, then some kettlebells, then BOSU, then medicine ball, then the rest.
That's my opinion, hope it helps.