Half circle cloak
Half circle cloaks (also called mantles) were a popular choice throughout much of the SCA period. Numerous survivng examples exist today, from the coronation mantle of Roger II of Sicily to the much more humble Bocksten mantle.
Half circle cloaks were pretty much the norm from about 1100 on, although scattered survivals of the earlier rectangular cloak (mostly among poorer or isolated peoples) continued on for some time. The more extravagant 3/4 and full circle cloaks seem to have evolved as weaving technology became more efficient, just like the rest of the world's fashion did.
On the wearing of half-circle mantles
At least one surviving example (the manto belonging to Fernando de la Cerda, at the Museo de las Telas Medivales in Burgos, Spain) has two ties, one on either side, which are rather farther down than you would expect. This matches this author's experience of wearing one, and actually helps to 'fit' the garment to the body so that it stays put. Also, when worn with pins or ties in this location, half-circle mantles hang in a manner that strongly resembles simialr items seen in 2 and 3-d depictions from period.
Personal anecdote of how simple half-circle mantles behave when worn:
"My heavy, fulled wool, winter mantle is a pure half-circle, calf-length, and is worn opening at the front, clasped with a heavy double pin (bridged by a chain of approximately 6 inches). It does not tend to slide down the back, but that is because the double brooch is pinned at shoulder level, /after/ arranging the cloak so that the extra cloth wrinkles up at the back of my neck (nice and cozy in cold weather). This is usually about 16-18 inches down from the crease when the cloak is folded in half.
My summer mantle, being a little shorter and of finer wool, can be pinned to my gown with lighter brooches and doesn't wrinkle up much at the back of my neck because the lighter fabric drapes more easily across my shoulders. It is light enough that it can be comfortably pulled over my head (in the veil/mantle manner) if I need to do so." - Lady Marguerie de Jauncourt
On decorating mantles
Nearly all of the surviving cloaks from period (And yes, I mean the whole 1000+ year stretch) that we have are decorated in *some* way. Some, like the 'Schnurmantel' and the coronation mantle of Roger II of Sicily are elaborately embroidered with designs that stand out from the base fabric, some are only 'trimmed' with embroidery (the Mammen cloak). The cloaks from the Burgos collection are decorated in that they are made of elaborately patterned textiles of Moorish origin.
Due to artistic (and some arechaeological) evidence of undecorated cloaks, iy is safe to venture that lower classes wore them. It is also likely that these would be unlikely to have survived as they were ideal candidates for recycling into other things (and also because the richer garments were given into the care of the Church after a period of secular use, which helped to preserve them).