It is practically impossible to keep certain projects spotless for the entire time that they're being worked on, but avoiding trouble in the first place is the way to start. Be sure that your machine is free from any kind of surface oil or lint, and consider covering the area under your worktable and ironing board with old sheets. Be sure there's nothing rough for a gown to catch on. When your day's work is done, consider storing your project in a garment bag. I often store big silk satin skirts, in progress, inside out in a garment bag.
Good tools are essential.
Not only will they save you time, they will help you produce a superior result. You and your project deserve nothing less. Not only is it strong, it won't kink or break the way inferior threads do. My favorite is a long staple polyester, which has a very silky feel to it. Measuring and fitting must be done with the correct undergarments and shoes of the height that will be eventually worn with the gown.