I'd personally recommend the Garmin etrex 10, 20 or 30. It has all the functionality you say you desire and can be found fairly cheaply on eBay (used). The 10 is the base model while the 30 can use a cadence sensor.

It might be possible to use a car-style GPS BUT battery life might be an issue (most won't last more than 4hours no matter what). That's part of why I like the etrex 10/20/30. Takes AA batteries and lasts 16-20 hours.

My recommendation is based purely on functionality and personal in-use reliability, not manufacturer snobbery. Also, I got a great deal on a refurbished etrex 20 which has more than met my needs and expectations.