Get a good set of free weights, and maybe a resistance band. Jump ropes are always a good idea, and I’d recommend going outside to run rather than getting a treadmill.
References :

Well here is what works best, honestly. Have you ever heard of P90X? It is on TV all of the time. It is a 90 day program of crazy workouts 6 days a week, and if you stick with it, you will be shocked at the transformation you will receive. Go to http://www.p90x.com It is much cheaper than gym equipment and works much better.

I used to workout at a gym. I would do bench presses and chest exercises for an hour. The next day I was beat, and sore.

I just started P90X and did their chest dvd on Monday, and let me tell you, it made my gym workout look like a baby could do it. P90X is out of this planet. I am still sore. Email me if you have any questions concerning the program at redbull9944@yahoo.com Ask me anything you want.
References :
p90x.com

Whatever is most effective is whatever you will use long term. Fat burned is determined by your heart rate. As long as it’s in that range, you will burn fat. I bought myself a stationary bike and throw that in front of my tv and pop in a dvd movie and pedal away. The fat comes off.

edit: OH YEAH! as the one person said, buy some weights!!!

To lose fat you need 3 things:

1) A properly designed diet (this is 80% of it)
2) Lifting weights (this is 10-15% of it)
3) Cardio (this is 5-10% of it)

Lifting weights is important during FAT loss because it (along with a good, well designed diet) will KEEP your existing muscles. This will ensure any "weight" loss is only fat. MOST diets I see lose muscle mostly. Maybe some fat too.
References :

I tried to lose weight for months before I was able to find a way to successfully lose weight. Instead of rewriting the article I found, you can read it here http://loseweight.newseek.info.
References :
http://loseweight.newseek.info

Saralahalawawa,

The honest answer to this question is very dependent upon you. There is no one size fits all equipment option that best suits you needs.

For the intro user I would highly suggest cardio equipment. While a treadmill can help you lose weight quickly, the impact on your joints (knees, hips, and lower back) can be more substantial versus an elliptical trainer, or a recumbent bike.

For the most intense workout and to shed weight the most effective way I would recommend products that incorporate total body movement to allow parts of your body to be exercised and all your muscles to burn fat.

In my personal option you should take a look at indoor rowers, Jacobs Ladder, and possibly a VersaClimber.
P.S. If you want the most intense workout at home, you can invest in a StairMaster Stepmill - depending on your cardio level 15-30 minutes will be enough to make you cry
References :
10+ years in the fitness equipment industry
http://www.gymstore.com/Rowing-Machines-s/278.htm
http://www.gymstore.com/Steppers-Stair-Climbers-s/277.htm
http://www.gymstore.com/Stairmaster-7000PT-Stepmill-p/sm-7000pt-lcd.htm