If you want to work out at home, you could get in great shape doing it. But you'll probably do very well to concentrate much more on strength building exercises than the typical home program, which is usually aerobics and stretching, does.
You can use bands and kettlebells and if you have the space, clubbells, and also dumbbells, as well as learn some tough bodyweight exercises, to give you a wide variety of resistance exercises.
At home or in the gym, I'd suggest you do at least one variation or equivalent of the squat or deadlift. At home, the deadlift you can do with jumpstretch bands very effectively(I have). Check
www.jumpstretch.com for bands and a handle. You'll only need the handle if you use the big 200 lb. strength bands, so most women should be fine starting off without them. This is a really great way to do deadlifts because you can lift the equivalent of a lot of weight without having to buy store and lift weights; it's just bands that weigh a few pounds and that you can throw in a closet when you're done.
The squats you can do with bodyweight alone, adding weight by holding a dumbbell or kettlebell or even a gallon jug or two of water, if it should ever become necessary. The one-legged bodyweight squat I'm speaking of is commonly called "the pistol," and requires some flexibility and balance. But this is great to develop too. In working on the pistol, you'll be working the front and back of your thigh, your butt, the muscles around your hip, and your calves all at once.
Check out
this link for a great article by Steve Cotter on the pistol. He even addresses problems and how to correct them very well.
There are lots of great bodyweight, band, dumbbell, clubbell, and kettlebell exercises for the upper body. Keep in mind that you should have at least one really tough push (moving stuff or your arms away from your body -- uses the chest, shoulders and triceps) and one really tough pull (brings your arms in to your body -- uses the large muscle of your back, your biceps, the muscle at the top of your spine that connects to your shoulders and lies between your shoulderblades, and your forearms and hands). Examples of a push: push-up, bench press, military press, dip. Examples of a pull: chin-up, pull-up, bent over row, putting a broomstick across the top of two chairs a couple feet apart then lying underneath, reaching up to the broomstick and using your arms to pull yourself up to the broomstick.
You can do all this stuff at home with minimal equipment that doesn't take up much space at all to get an excellent work-out in less than a handful of exercises. Adding more exercises in may or may not be helpful, but you should at least retain as the base of your program, in gym or out, a tough version of the compound exercises what I noted above -- one for the legs, one for the pushing muscles of the upper body, and one for the pulling muscles of the upper body.
Btw, once you start lifting heavy weights with your legs, unless you are on a machine, your waist will definitely get a heck of a work-out. And if you want a truly amazing butt and legs, like most women do, don't let anyone chase you away from the squat and pistol. They'll make you strong and sexy both.