Generally speaking, the closer to the period fabrics you get, the better the finished project will look. Period fabrics can be difficult to find, expensive and are in short supply. The range of fabric weaves in the period correct fibers are significantly less than what was available in period.
What does that mean for you? You have to make a choice on what is more important to what you are trying to achieve with your outfit. Is it necessary to be as close to period correct as possible? Is it better to look right than to actually be period correct? Generally the answer lies somewhere in between.
Fiber -vs- weave. Fiber is the content, weave is how that fiber is woven together. Fiber examples are: linen, cotton, rayon, silk, polyester, nylon. Weave examples are: plain, twill, herringbone, satin, velvet and jacquard. You can have silk velvet, polyester velvet or cotton velvet. The fibers are different, but the weave is the same. Conversely, you can have silk satin, silk twill, silk brocade, silk organza, or silk chiffon (to name a few). All are the same fiber, but different weaves.
Linen, silk, and wool are the most common period fibers. Cotton was still expensive and not in common use in the European areas yet. There were more weaves readily available in linen, silk, and wool than there are today. Polyester, rayon, and nylon are modern fiber inventions.
Cotton as a substitute for linen. If your shirt, shift or chemise is going to show, I suggest splurging on at least a linen blend if not 100% linen. Nothing really takes a crease like linen does, and it was the most widely used fiber for undergarments because of its durability. I understand that linen can be prohibitively expensive or not available in some areas. Cotton is the next best thing. Hemp and bamboo fabrics can be substituted for linen, but they are usually less available and more expensive than linen.
Brocades can be tricky. For light weight ones you can add an interfacing. The light weight ones can tend to be a modern or oriental design that you probably wouldn’t find in a 16th century English town, so beware of the pattern. Designs should be fairly geometric or non-photo realistic. You also don’t want to use one that is so heavy that you can’t handle the weight of it as a garment.
Prints were rarely ever used in clothing in this time period. At the time, the technology was new, expensive, and imperfect. Nothing like today’s inexpensive cotton prints that are so easily available. Sometimes a print can be the only way to get the look you want without compromising your budget. A lot of times a print can give a good approximation of period all over embroidery or brocades that are not as easily available today. (MET English Embroidery of the Late Tudor and Stuart Era)
Shopping in the home decorating area of the fabric store tends to be where the heavier or more tightly woven fabrics are. They can be great for outer layers, but you want to be careful of any backings or interfacing that may come on the fabric. Sometimes the interfacing can be what you need, other times you’ll need to find a different fabric, or only use it in places where you need that extra stiffness. Some of the backings may be inappropriate for anything on the body, and are only good for upholstery, or possibly some accessories. So before you fall in love with a home decor piece, turn it over and check the backing.
Colors are a very personal choice. While modern fluorescent colors are extremely hard to get and keep by period methods (Check out the history of aniline dyes in the 19th century), there are plenty of natural dyes that can make a wide range of colors.