I don't have a lot of different experiences with HRMs for cycling (could give you a bit of input on running HRMs), but I can say that if you're interested in accurate calorie counts, you'll need a chest strap and not an optical wristband. The calorie algorithms are based on the heart's actual electrical signals (R-R interval), which optical sensors can only guess at.

I've used the old Garmin hard strap for years with almost no problems. It's reliable, durable, comfortable. Can't say the same for their newer designs. But, being an older design, it transmits on ANT+ only, so if you plan to use it with your phone rather than with a bike computer, you'd need a dongle. With newer Bluetooth straps, you'll need a phone that's capable of Bluetooth Smart (aka Bluetooth LE, I think the version is 4.0) - most phones produced within the past couple of years have that, but be sure to check.