Before you spend money, you should make a preliminary decision: If you are interested simply in reducing weight, you really only need a rough indication of your output level (and thus your caloric consumption) to help guide your exercise level, and a HRM is just fine for that. A power meter can do it too, even a cheap one, and they inevitably measure HR anyway, but you are getting information you have to learn to use if it's going to be of any assistance to you and at that point you are probably wasting money. Either device substitutes numbers for a subjective feeling of "I'm gutting myself today" or "I'm not."
So ... you're in a forum here with a bunch of people who count tenths of grams and tenths of watts. Obviously you don't have to be so .. weight weenie, if we dare use the word ... to improve and become a superb rider. However, is that even your objective? If you just want to ride above a certain threshold so you can burn fat most efficiently (hence the question about target range, and about it being narrower than what you cited), a HRM can do it reasonably well (say +/-10%). For a rider who wants to measure his performance in a racing context, that 10% means you may be overdoing it and wearing yourself down half of the time and may not be working as hard as you need to half of the time -- not by much, but enough that you aren't going to become your very best. If you are riding at your aerobic limit, +/- 10% is the difference between gasping and burning out on a ride, versus riding at a conversational pace and not burning quite as many calories.
Some of us, the undersigned included, like to work out at the limit. Many people can do that without a power meter and frankly, once you've used a power meter for a while, you have a pretty good sense of how your body is feeling and whether you are riding at so many watts or not. I may put away the power meter part of the year if my goal is not to tune that last 10% right then (and you can't really expect to ride that very top 10% or closer all the time, or you do just wear yourself down). But that's about race training or about fine tuning a fitness plan that you have assessed and experimented with and refined.
I don't sense you're there. So my recommendation is basically to read some literature on power meters and threshold testing and all the other jargon -- there are a couple paperbacks on power meters, plus a number of websites (Google's Wattage forum is there if you are at the point of tattooing your wattage numbers up the side of your cheek), and so on. To use a power meter or really to understand target ranges and thresholds in any refined way, you have a lot of learning to do. Until you have that commitment and level of interest, a HRM is more than enough. If you can measure HR, miles, and perhaps cadence, you are going to be pretty happy with your results because you will push yourself onwards -- not necessarily to what you could be capable of, but enough to lose weight and enjoy the process. Any of the Garmin bike units works well for that and they're pretty much indestructible, plus the recent versions tend to be compatible with just about everything. Wahoo is coming on strong but you want your display to be on your handlebars, not in your pocket, so just getting a sensor that feeds your iPhone isn't as useful unless the iPhone goes on your bars. There are other brands like Suunto and Polar, and they work well enough but my only proviso is that they often aren't compatible with the major trends in HRMs and power meters. So why buy something that doesn't have a future as you improve and want more? Remember, yes, this is weight weenies (now I've gone and said it) and if you're here, you're about to become an addict to bike equipment. You'll end up with that power meter. And probably an expensive one. You'll sell a kidney for it, or your oldest child if you are truly serious (though losing the kidney does save weight on the bike). But for now, for you, I'd just learn and start simple. You'll lose weight and be able to decide what you really want before you start spending a lot of money. Make the power meter a reward for losing 20 lbs. If I had done that enough, I'd float by now.