Heart rate monitors are fab, but I'm personally not convinced that they are good for attempting to calculate energy expenditure, they are not that accurate, and even if you get a reasonable one, the energy you will burn through exercise is so insignificant in the scheme of things, it's sometimes better not to know, and just enjoy the exercise for what it is, a good healthy thing that may help you get towards your weight loss goals a tiny bit quicker.
But for performance training, a HR monitor is well worth the money.
Just to back up my argument. Relatively hard running burns in the region of 500 calories an hour, perhaps a little more if you can really run hard, 'most' people can't especially if overweight. To lose 1 lb of fat from running it will take you 7 days, 7 hours of hard running for a measly pound.
You would end up overtrained and injured in no time doing that.
Brisk walking - around 200-250 cals per hour, and at a level where fat will be the primary fuel source.
Sitting in bed and not moving at all - Around 56 calories per hour for a smallish female.
Doing normal daily chores, walking, housework, fidgeting - probably around 80-90 calories per hour avg over the day.
So, brisk walking a few times per week with a moderate calorie deficit is by far the best way to lose fat. Cardio is not great for it, you also get more hungry.
Weight training is good for the increase in lean muscle mass and they increased metabolism as you get more muscle. Not huge, but you get the benefits all the time.
You burn fat all day, it is the 23 hours that you are not exercising that counts.