Garmin is certainly the dominant and preferred device of TrainingPeaks. There are many other devices that athletes enjoy, but the capability between 80/20, TP, and Garmin is pretty slick.
If you have a device that accepts the TP structured workouts (like Garmin) then yes, when the workout is synced to your device (either manually or automatically) your custom zones are also delivered to that device.
If you are a triathlete, the Garmin 735xt is a solid, all-around watch. If you are a runner only, the 935 or 945 are great options.