All my bikes are in use so a complete period correct rebuild isn't practical. I tend to stick with parts that look like they belong with the bike and it can often mean this is very much dependent on the frame. Some examples:
-My main bike is a mid 80's Russian track bike. I bought it as a frame and there's no way I'd ever be able to find original components for it. It wears almost all brand new but retro-looking components, so Andele track chainset which looks like the original, new track hubs laced into box-section polished rims, tan wall clinchers, Cinelli 1A with 70s curly Dawes bars, plain alloy seatpost with a Unicantor and a modern brake. So to the untrained eye it looks pretty period but it isn't.
-My geared bike is a late 70s Bob Jackson frame with all the running gear off a mid-90s Raleigh Strada, so it's Shimano Biopace, 105 aero levers and semi-aero alloy wheels. To my eye it doesn't look out of place.
What I mentioned about components that look like they belong; the frame cracked on my geared bike recently so I need to replace it. I'd only use those components on a frame from 70s up to 90s. In my eye, they don't look right on earlier frames from the 60s and they belong on newer frames from the 2000s. Older components on a new frame don't work for me. Likewise, I wouldn't expect an Italian frame to have ever had Shimano components, so I wouldn't put them on an Italian frame.
I find for my older bikes it becomes a bit harder to do a period build. Original stuff is really scarce and can be expensive I've got two 1930s frames but neither of them came with any of their original components. One was a bare frame and the other has received a complete rebuild with new components in the early 50s. This was quite inspiring for me, because the in 50s cycling was taking a boom and there are stacks of components available. It was still a time of austerity and they don't look out of place on the older frames, particularly if you choose lower end stuff, so in my mind it is quite legitimate to build a rough 30s frame up with lower end 50s components in good condition. I kind of see it like something a less well-off club rider might have done, or a kid building up his father's or grandfather's bike with what he could afford.