I like to de-prime brass first. I use a Lee universal decapper, which does not touch the brass. Only the de-capper pin on spent primer and and the shell-holder get touched. Then I clean in either a SS tumbler (cleans primer pockets), or hot dish-washing detergent/water. The wash water removes GSR, and leaves brass clean for handling and sizing. The brass drains well without the primers.
I use a pad or paper towel and very lightly lube rifle cases with White Lithium Grease, and only lube every other, or every third, case. Some grease sticks in the die, so I do not need to lube every case. They size very easily (even military 7.62). I have never had a stuck case with WLG. It does need to be cleaned off by washing again. I do not lube 40SW and 9mm handgun brass, and don't use carbide dies. Regular Lee dies work fine for those.
Notice that to this point I have not used dry tumbling media, so I do not get clogged flash holes. I may tumbler for appearance, and may need to poke some flash holes, at that time, if I do.
I find that 223 don't need much trimming, but it is easy enough to set a micrometer at a hair over trim to length and use asa trim/no trim gauge. 7.62/308 I need to check with a case gauge every sizing.