Since we are trying to recreate archery as it was practiced during the middle ages (i.e. "Period", or approximately 400 A.D to 1600 A.D.), in central and northern Europe (possibly with visitors from other areas). So, no compound bows, no sights, no stabilizers, etc. None of the conveniences that modern archers take for granted.
Most people I shoot with, use (modern) fiberglass and wood composite recurves, with center cuts to shoot through. While this isn't really very period, they are easy bows to find, sometimes relatively cheaply. Most SCA archers shoot bows between 35 and 50 pounds draw weight. Several people have "Longbows" that are also made of fiberglass and wood. Crossbows are also allowed in SCA shoots, however there are many ranges which do not allow them.
One of the most common shoots in Caid is called the "Royal Round". This consists of 6 arrows shot at a standard 60cm 5-color target from 40 yards, 6 arrows at 30 yards, 6 arrows at 20 yards, plus a speed round. In the speed round, each archer starts with an arrow nocked and has thirty seconds to shoot as many arrows as possible (or as desired). Scoring is 5 for a gold, 4 for a blue, and so on, down to 1 for white.
One reason the Royal Rounds are so popular is that these scores are used to determine ones ranking. The best three scores for any given year are averaged. The table below lists the ranks and the scores needed to attain them:
Rank Scores Novice 0 - 24 Bowman 25 - 44 Yeoman 45 - 64 Forrester 65 - 84 Bowmaster 85 - 104 Royal Bowmaster 105+
English style longbows (which is what most people think of when talking about "Medieval" archery) used the natural properties of a particular tree, the Yew tree, to achieve the same goals as the composite bow. The heartwood of a Yew tree is yellow or orange in color and has a high compressive strength. Whereas the sapwood has a high tensile strength. The bowyer used these properties of Yew to make very powerful bows, possibly as high as #180. English longbows were made with a slightly rounded "D" shape which was generally very thick from front to back. This thickness contributed to the bow's power, but it also made it more likely to break. To counter this the bowyer needed to make the bow longer, hence "Longbow".