The key on vintage sets on hair is doing a wet set. This is how I do my hair when I do vintage styles. I have a section of hair that HATES taking curl. So the day before I need to have my hair in a vintage set, I wash my hair and use Motions setting mousse. I leave it in for a full day and then the next day my hair is a tad dirty, I then use Lottie Body setting spray in a two parts spray to three parts water. I have used foam rollers, pillow rollers and have done pin curls with clips. I've found the pin curls with clips work the best for me. I usually sleep in the pin curls and have a sleep bonnet on like in the old movies. I then use a Denman Brush to brush the curls out. I use One n Only Argan Oil Spray Treatment to eliminate frizz. And LayRite pomade to help sculpt.
I agree that wet setting is the best, and Lotta Body rocks, but you don't always have time. You can get a good dry set with hot rollers if you use Redkens Hot Sets 22 spray - it's a thermal protection spray that will set your curl without making it too crunchy. Spray it on each section as you put it in hot curlers or curl it with a curling iron. If you are curling with a curling iron, make sure you pin each section until completely cool, then brush and style with a good brush. I like Chi Silk Infusion to reduce frizz. All my studies of vintage hair styles is to brush and keep brushing until you get it to do what you want it to do - use your brush to curl the hair around your hand, and be patient!
I always set my hair dry with foam rollers (wet sets don't work because my hair takes FOREVER to dry - and a damn curl is a straight one). I use Jane Carter foaming mousse and as I section my hair I put a tiny bit of mousse on each section. It isn't crunchy and really helps my curls hold. I then wrap my head in a scarf and sleep on it. My hair hates taking curl (heat sets don't even work on me) but these sets last for 2-3 days (re-rolling at night). Here I am after styling -