I've never seen a particular need for synthetic in normal applications. Supposedly they give you better mileage, but the difference is going to be too small to measure. If it's big enough to measure, your axle would be running red hot. Claims are that the synthetic does not mix with water, such as you might pick up in a water crossing, but most recommend changing the oil after big water. I will be a lot more likely to change cheap fluid than expensive synthetic.
As for the breakin procedure, like the man said, don't let it overheat. Several times I have installed gears and headed out to Moab. I just check them every 20-30 miles for the first hundred and then just drive them. I change out the fluid when I get back. More important than fluid type is getting the gears set up correctly the first time.