This particular area of re-enactment has changed, in my opinion, more than any other. What was once acceptable is now cringed at, so the best and only thing I recommend is don't buy anything unless it is 100% linen or wool.
The fabrics used during the medieval period we portray would have been either wool or linen and that is what all of the following guidelines will recommend you to use. Cotton and Silk were only available to the exceedingly rich.
Getting the right material can often cause problems for new members, so I would recommend asking someone more experienced to help you shop for it. There are several re-enactor markets throughout the year, as well as mail and internet order places that will be able to supply your needs. There is always a good Historic Traders Guide within the group if you're struggling. I would recommend that you plan out your material needs and buy material when it is available, as it is much better than wanting to make kit and having no material.
Another material that can be used is fur, for most of us sheepskin and rabbit are the practical ones. There are other furs that were used by the lower ranks but the two mentioned are the easiest. Furs can be purchased cheaply in charity shops; you need to ask for them as they are not normally on display due to animal rights issues. Fur was mainly used for trimming garments such as gowns and doublets, around the neck, cuff and hem. Fur is cleaned best by brushing it, as this will remove mud and dirt it has collected. Needless to say, the better furs were reserved for the wealthy and, as such, fur should be used in moderation. When constructing your garment, think about whether it is suitable for the elevation a fur trim would give it.
Fabric weight is also very important. Heavy fabric moves differently from light. Medieval people wore several layers of clothing at once, so try and think how you will use your garment when buying the material. For shirts and shifts, purchase shirt weight or light weight linen. For dresses and doublets, you need to think about which layer the article is for; if it is for inner wear use lighter linen or wool, for outer wear use a heavier weight fabric. Lighter weight wools can be used for pour points or inner doublets. Hoes need a wool that will stretch on the bias (45 degrees to the edge of the fabric), this is important otherwise they will split. Linings are used extensively; they should be heavier than shirt weight, but not as heavy as the top fabric.