You have a number of options for doing this.
- Join the MFI program and either read the input via a physical connector or via Bluetooth.
- Use Wi-Fi. Probably easiest in terms of programming but requires more expensive hardware (and maybe more complicated installation)
- Use BLE (Bluetooth Low Energy) and CoreBluetooth. Cheap, easy to use.
As you have already suggested, BLE is an easy way to go that doesn't require joining an expensive program. The Bluegiga chips are excellent in talking with an iOS device (I have personally tried the BLE112 device) and they are easy to program, comes with their own microcontroller etc.
To start on the iOS side, you need to read up on CoreBluetooth. Apple has in general excellent documentation about this framework.
I would recommend starting out with the examples, for example the Heart Rate monitor sample project. Also consider buying a dev kit from Bluegiga, it has among other things, a Heart rate device sample that works with iOS.