The two main device types are smart phones with cycling apps and dedicated cycling computers. If you already have a smart phone then getting an app such as Cyclemeter and compatible sensor(s) (heart rate, etc.) are a good option. There are pros and cons for both device types.

The Garmin Edge 500 is a good entry point for those interested in a dedicated computer for training purposes but don't need street maps. It's MSRP is $200. Check it out at Garmin here or read an in-depth review by a master here. Garmin has added a few enhancements to the 500 since it came on the market 5 years ago.

To monitor heart rate you'd need to add an ANT+ strap such as the one Garmin sells. Some riders also want the cadence and speed sensors. They're all sold separately or as a bundle.

Note that most sensors that work with the iPhone use Bluetooth, while most dedicated cycling computers use ANT+. That means that the sensors aren't interchangeable.

Other dedicated cycling computers add street maps, and other features. For basic training data up to and including power meter readings (power meter not supplied) the 500 is one of the cycling standards.