First, let me preface this by saying I know next to nothing about shotguns. And don't shoot them well, either. Anyway,
A friend had an old Ithaca pump gun that the stock had cracked on and I offered to repair for him. On disassembly, of course the inside was coated with 40 years of gunk. After much scrubbing, it's -relatively- clean and dry. Question, what the proper way to relube for assembly? I had thought about just spraying it with Remoil, but got to thinking that might just attract more gunk than it had...

You can learn a lot ffrom military rifle shooters.... They almost never use oil, but rather grease. There are two that i use. I use a product called lubriplate, a white grease for short term applications, like on my shotguns where I'll take them down and clean and relube. Another grease that I use is a synthetic from Brownell's called Action Lube Plus which hold up well for extended periods of shooting. I use the Action Lube on my Garands.

The best oil you can buy with American cash is Auto Transmission Fluid (ATF).

An all cotton sock or piece of sweat shirt stored in a sealed jar with VERY few drops of ATF on it will leave barely a trace of oil on the steel parts.

"The proper amount of gun oil, if applied to a shot glass, won't ruin good whisky."

Thanks for the tips, folks!