Masking tape is your friend.
Word of warning though, don't leave it on more than a week or so. It will cause grief!
I have over 30 guys in my restoration shop, and even with the most careful procedures, yes you do get some chips and marks now and again.
Pretty hard to compress a coil spring without making some marks, but you can minimize it by using some gasket paper or scraps of leather to line the shoes of the compressor. Of course you have to be careful that nothing slips!
Soon as you unwrap chrome, with clean hands (even a little dirt on your hands or bench will scratch new chrome), tape it up. Use good quality low tack tape. Never slide a chromed part across any surface/table (even a padded one) without the part being fully covered in masking tape.
Set up a specific part of one of your benches with soft vinyl on top to handle all your fine assembly jobs- dash, guages, etc.
Someone was right when they said material thickness of the paint affects its resistance from damage. Thin is good.
We use a lot of upholstery vinyl scrap on doorsills and doorjams during assembly- prevents feet scuffing, airhose rubs, trouble light cord rubbing, etc.
Pretty much need to spend some money on some protection materials- good quality fender covers, new rags (not clean used- they have bits of metal sometimes), good tape, not cheap and lots of scraps of foam and upholstery materials to protect your new finishes.
And after you're all done, a polish job is necessary.