Every 6.0L owner needs a monitor IMO.
Oil and coolant temperatures are very important to watch. The differential between these two temperature readings tells you when the oil cooler is plugging up.
Lots of threads on multiple 6.0L forums on monitoring the 6.0L.
You should also keep an eye on FICM voltages, boost, and ICP vs IPR % duty cycle.
You don't necessarily need to watch things all the time, but it is helpful. To have the ability to watch things periodically, you can download ForScan Lite to a smartphone for $5-$10 and buy an ELM327 OBDII adapter for $35 or so and be all set. ForScan is a very good code reader also.
The ELM327 device needs to be WiFi for Apple phones and BlueTooth for Android.
If you want continuous monitoring, the SccanGaugeII is a common choice, but it is kind of clunky and is around $150.
You can go way up in cost with monitors from Edge (CTS2, etc).
I also advocate to watch fuel pressure. The leading cause (perhaps behind Stiction) for injector failures is low fuel pressure. To get a fuel pressure reading you need the sensor AND the gauge. Our engines did not come with anything to read fuel pressure. It is important though. It can save you thousands of dollars to catch low fuel pressure BEFORE the injectors are trashed.
