Many of the patterns from the '50s and '60s (and some of the earlier sewing patters as well) were designed to be worn over specific undergarments. In the case of women's garments from those decades, this usually means a girls or petticoats, sometimes even both. If you're sewing a very fitted garment that is designed for use with a girdle, you may have to add more ease to both the waist and the hips. If you want the iconic look, you might want to try a girdle.
Most of the vintage patterns you'll find look perfectly find without any special underwear. In fact, you'll look more like you're wearing clothes and less like you're wearing a costume if you just wear whatever you would normally wear. If you like a push-up bra, wear it. If you hate garters, ignore them. Wear what makes you comfortable.
This is true of just about all vintage clothing, unless you want to achieve the full-skirt look. If you really want full skirts, you'll have to wear petticoats. Don't bother with the hoop skirt (they're uncomfortable and unwieldy), but do buy or make a few good-quality petticoats. Before you hit the town, however, practice wearing them around the house. Modern women aren't used to petticoats, and they do change the way you move. A few hours should be enough time to acclimate yourself to the feel and look of voluminous petticoats.
How many petticoats? That's up to you. More petticoats means a fuller skirt, but it also means you'll have more difficulty moving around. Try adding one at a time until you get the look you want.