Hi Fred,
Congratulations on entering the exciting world of tractor owning/operating!
#1. Read the manual. Read the manual. Read the manual. Get to know your machine.
Take the manual to the machine and familiarize yourself with what you learned about reading the manual. Check the torques listed in the manual for everything listed. Check them at the intervals the manual states you should. Note the locations of all the grease zerks, fluid checks, and drain & fill points.
Get the fluids & filters the manual calls for (or equivalents), and the tools needed to change them. Change them at the intervals the manual specifies--Some do right away to get out any "post manufacturing" bits floating around in the first fluids.
Personally, I clean the outside of the engine as often as possible, for the same reasons you do any engine... compressed air usually, with water when needed... engines cool better without an insulating layer on them.
I probably have a DSM condition when it comes to maintaining vehicles... also the compulsive tool-buying... but it keeps them running smooth.
It is a machine, like a car or truck, outboard, generator, furnace, etc... get to know your machine & follow the maintenance guidelines outlined in the manual and it should give you years of trouble-free service.
Did I mention the manual???