I like sonic cleaning, then spray lube outside of cases and use a sizing die set up with carbide expander. With the inside of necks clean, carbide expander eliminates the need to lube the inside of case necks.
I use Redding neck bushing dies for most of the ammo I plan on shooting for in my bolt guns. I think the Redding die is far superior to Lee. I have found it best to make sure case neck walks have equal thickness when using bushing dies.
I used to use media all the time for cleaning cases. With a good sonic cleaner, it has been over a year since I used media to clean cases.