For the engine oil, use a good quality synthetic oil that exactly matches your vehicle manufacturer's specifications and certification requirements, and change it according to the vehicle manufacturer's recommendations. Contrary to popular belief, very few people actually know better about their engine than the people who actually made it. The old rules about engine oil intervals only apply to the old engines. When in doubt, rather than change it too early, which increases chances of some of it getting into a landfill and only adds to oil imports, get an oil analysis done. If you drive mostly city traffic or short trips, then changing the oil more frequently is warranted, but if your driving is mostly longer trips, especially on the highway, then 10,000 miles or longer, whatever the vehicle manufacturer recommends, is all that's needed. For extended oil change intervals, changing the oil filter at the mid point between changes will help keep the oil clean. Not that big a deal with gassers, but it is with diesel engines.
For the transmission, same thing, go with the recommendations to be found in the manual. Same thing applies to city (lots of shifting) and highway (mainly in a single gear) driving where you can extend the interval or not, depending. Most expediters can extend the transmission oil change without any problems. At the very least, changing it prior to the manufacturer's recommendation is simply wasting money and oil.
As for the differential, most manufacturers recommend changing it about twice the interval of the transmission, but again lots of highway mileage is the important thing, and in this case suggests more frequent changes for the differential. I change mine every time I do the transmission.
If you want to deviate from the manufacturer's recommendations, don't do it based on
"common wisdom" or because that's how you've always done it in the past. Do it because you know and understand why the manufacturer recommends certain things, and will then know and understand why any deviations are or are not warranted.