The purpose of costume is two-fold, in my opinion. It visually puts the audience in the proper time period, and it gives insight into the character. For an example of character costume, Lady Catherine DeBurgh in "Pride and Prejudice" is not going to wear the same Regency fashions as the young ladies. She is old and conservative, and her style is of a bygone era. If you were to see her all by herself, without the context of the story, you would think she was from the late 1700s rather than the early 1800s. She does this proudly, as if the modern styles are merely a passing fad and the young will eventually return to the sanity and reason of the past. Similarly, Cecily in "The Importance of Being Ernest" is not going to wear gingham. It is associated with children's clothing and kitchen curtains, not with the toilette of a gently-reared young lady. Henry II in "The Lion in Winter" is not going to be decked out in velvet and silk. Such fabrics were very costly in the 12th century, and would have been used in small quantities for decoration, not for an entire garment. It is important to remember historical details. Girls did not wear pants to school before 1970. Things we take for granted today have not always been there.
When dressing a period play, how far do you want to go? In many cases the answer is, as far as time and budget allow. If period fabrics are not available, it's better to try and find something that looks right than to substitute something that looks modern. Usually, it is not possible to hand stitch everything, so there goes your period accuracy right there. I don't have minions who will stay up sewing all night in exchange for a crust of bread. So, we adapt our ideas. It sometimes takes research to find out what the fabrics even were, as they had different names--samite, tarleton, sarcenet, linsey-woolsey. There weren't zippers until the 1930s, though the things were invented maybe 20 years before that. We didn't have terry cloth till then, either.
I once read an article in a magazine for weavers that chronicled the efforts of costumers to reproduce the exact drape of Greek robes on vases. They had to develop a whole new blend of fibers to achieve this...even had to throw some synthetics into the mix. Like they really had polyester, back in Ancient Greece! Still, the drape was what they wanted and the drape was what they got.
I usually try to avoid being a slave to Period. For a parody, such as we are doing right now at Sam Bass, it is sufficient to suggest period. Tying sashes above the waist on fairly narrow gowns, for instance, will suggest Regency. Our play is "Mrs Bob Cratchit's Wild Christmas Binge," and the Regency (Fezziwig) scene is very short, as is the time the actors have to change from the Dickensian Cratchits to the Fezziwig guests. I made tailcoats for the men by cutting suit jackets and trimming with seam binding all around. Old Fezziwig's wig is made from a Santa wig that I curled up with bobby pins and netted. Sufficient for our purposes. I will have pictures.
Some plays (serious ones, usually) require careful attention to period details, especially in our intimate space at Sam Bass. Between the 1920s and 1960s, for instance, ladies' stockings had seams. Not the knitted-in "seams" you see in stockings you get from a purveyor of sexy lingerie, but real seams. If you can't get them, you need to have your actresses draw straight lines down the backs of each others' legs and spray them with hairspray as a fixative before putting on modern hose.
Most of my costuming is in community theater, where we have neither time nor budget to build everything from scratch. We adapt existing garments. The late 1960s produced a lot of nice suits. Carnaby Street may have a lot to answer for, but that Edwardian look popularized by many of the rock bands of the era is a costuming gem. The jackets work almost perfectly, and all one has to do to the pants is take them in so that the bell bottoms disappear. Similarly, the high-waisted narrow dresses favoured by girls at time make lovely Regency gowns...early Regency, anyway. For later Regency styles, all they need are gathered overskirts attached at the Empire waistline. When hitting thrift shops, yard sales and estate sales, the astute costumer has a constant eye out for clothes that can be easily adapted and for curtains, bedspreads, tablecloths and other things that can be sliced and diced into doublets, flapper dresses or biblical robes.
You want to avoid obvious anachronisms, such as pants with creases if your play is set before 1892. That date needs to be carved into the memory of every costumer. That, Dearly Beloved, is when the pants press was invented, and, since then, all men's business and formal pants have had creases. Before that...not so much. Oh...and pockets. When we did "Hamlet" set in the Regency period, we couldn't afford to make all the pants without front zippers, so I bought the pants, ignored the zippers and sewed shut the pockets. No gentleman of that day would have spoiled the line of his hip and thigh by putting pockets there. Gentlemen of that day would have loved Spandex! Actually, modern jodhpurs make very good Regency pants.
I have heard it said that the best costumes are pretty much invisible. Ideally, the audience should just assimilate the information they provide without really noticing them. So do your research, look at as many pictures as possible, learn who wore what when--and have fun.