Heart rate monitor

Which iPhone?

All the heart rate monitors with Bluetooth Smart are compatible with iPhone 4s and there are dozens of great apps on App Store as well. Just decide for yourself which type is more appropriate for you (chest strap + iPhone, chest strap + wristwatch + iPhone, strapless wristwatch) and look at the numerous items on Amazon. Make sure there is an option with sound alarm if you are out of target heart rate.
There are also many topics here devoted to heart rate monitors so better use search in community.
Good luck!

Realistically, you will generally get what you pay for, but you can often save money on the same product if you shop online. I picked up a Polar RS300X around a month ago for $90, and it does the job decently enough. Most heart rate monitor straps will cost $65-80 anyway, and the watch based "training computers" will be more convenient to check your heart rate than checking your phone as you are working out.

You really have three types of monitors available. There are the "Strapless" type, the ones that are a watch and come with a heart rate monitor chest strap, and then you have the chest straps that connect via Bluetooth to your phone. The ones with the chest strap will almost always be more accurate. Not needing to pull out your phone while working out, and just looking at your wrist will be the most convenient. If the strap would cost $60 by itself, and you pay $90 or so, you see you are not spending a ton of money for the watch, and it is MUCH easier to check your heart rate than checking your phone.

One thing to consider is that calorie burn estimates will always be more accurate if the system takes your heart rate into account. Many programs won't take heart rate, or even speed into account when it comes to calorie burn, and it makes NO sense that the same person running the same distance will burn the same amount of calories if they run the distance slower or faster. More effort=more calories burned. Dragging around more weight increases the effort it takes for the same exercise. The more effort your body has to put in to doing exercise, the higher your heart rate will be.

So, consider what you NEED from a heart rate monitor, and then use that to pick which one to pick up. Save your money if you need to. As I said, I picked up the Polar RS300X, because it has most of the features I personally was looking for. The only thing it doesn't do is save your heart rate over time during a workout, so all it saves as a log is max heart rate, average heart rate, and how long you have spent in each sport zone. Seeing the graph that shows how my heart rate has gone up or down during the workout would be very useful to me, but at the time I bought it, I didn't see the need for that. Some who cycle may want different features than those who run or swim. Some will want a GPS in their "watch", or to buy an accessory to provide that functionality, some will do what I do, which is to use a workout app on my phone, and I set it to start the workout 15 seconds later, with an audible countdown so I can sync the start times to the watch close enough together for my needs.

Finally, I've mentioned that I bought my monitor online for $90, with the sync accessory for an additional $40 or so. That made the price I paid for both monitor and the sync accessory(Flowlink) the same as for the monitor itself would have cost at a retail store($135).

I hope this helps.