I do NOT have any backache problems, nor any pain in the joints. Recommendations please, keeping these points in view.
You have some good answers already so I will just add to the list and give you some other points to consider:
Regularity - Increasingly studies are showing that Regular Exercise:
"can improve mood in people with mild to moderate depression. It also may play a supporting role in treating severe depression."
The key is being regular. Convenience, positive feedback and doing something you enjoy will help you keep more regular with your exercises. Also, having a partner or exercise buddy can help you keep going when you don’t want to exercise.
Convenience - Since you want to stay indoors, consider a home piece of exercise equipment if you have the room, like a treadmill, bicycle ergometer or an elliptical trainer for a good cardio workout. It is best if you do not have to set up or disassemble equipment.
Positive Feedback - Charting or logging your workouts will give you positive feedback, keep you to your schedule and motivate you to continue. Keep track of your frequency and length of sessions, amount of weight used, reps and sets, heart rate and make any comments you feel are relevant.
Exercises you Enjoy - Try out different types of exercise at home to see what your what you like and what your body enjoys. Exercise dvds from Netflix, Blockbusters or a video download site is an inexpensive way to try out a lot of different types of exercise. You can try everything from Aerobics to Boxing, Salsa Dance, Tai Chi, Yoga, Weight Lifting or Zumba right in front of your TV. (I tried a Qi Gong dvd and was surprised to find that my body loved it!)
The UT Southwestern study found that different levels of exercise intensity are effective for different people:
“Moderate exercise was more effective for women with a family history of mental illness, whereas intense exercise was more effective with women whose families did not have a history of the disease. For men, the higher rate of exercise was more effective regardless of other characteristics.”
To give you an idea of an effective schedule of intensity and frequency, a study in 2005 found that:
“ walking fast for about 35 minutes a day five times a week or 60 minutes a day three times a week had a significant influence on mild to moderate depression symptoms. Walking fast for only 15 minutes a day five times a week or doing stretching exercises three times a week did not help as much. (These exercise lengths were calculated for someone who weighs about 150 pounds. If you weigh more, longer exercise times apply, while the opposite is true if you weigh less than 150 pounds.)”
A heart rate monitor will help you determine the level of your exercise intensity and your exercise target heart rate.
Breathing exercises, relaxation and meditation exercises are also helpful to reduce stress. As Lauren pointed out, yoga is an excellent choice as it encorporates all of these.
Any kind of exercise can help relieve stress, depression, and anxiety by releasing endorphins and providing a distraction, among other things. I'd imagine that yoga would be particularly good, since it concentrates on breathing and mental relaxation as well as physical exercise. It's also good because it doesn't require any equipment, and you can do it anywhere, including in your own home. You might try some body weight exercises too, if you really want to stay inside.
However, it may actually be more beneficial to exercise outdoors than indoors. According to this article:
compared with exercising indoors, exercising in natural environments was associated with greater feelings of revitalisation, increased energy and positive engagement, together with decreases in tension, confusion, anger and depression.
Not to mention the fact that you'll get more social interaction if you go outside.
I see others recommended getting outside, I'll stay with your specifics of indoor stress and depression focus exercises. I would recommend that you get a heavy bag, some good bag gloves and tack out what you need to on the bag. There's a lot to be said for contact reducing stress (aka beating the heck out of something)