Fur would be the way to go on that one, I'd say. Lace, unfortunately, came along later. Fake fur is fine, though. People were making fake fur as early as about the 8th century or so (though to be honest in those days, it kinda looked like a sheep exploded onto some burlap, but it was the Norse doing it, and I don't think they minded so much).
For the cloak, I'd suggest a cotton or, more properly, linen, unless you need it to be warmer, in which case, wool is the way to go. A fur-trimmed cloak is an exellent way to go on that, as well. Woven or braided trim is fine, as well, but sometimes a little harder to find. Most fabric stores have some, but a favorite source of mine for trims is
Calontir Trim. For the time period , you'll want to steer more towards the non-metallic trims.
Another way to go on trimming, if you really want to get elaborate, is to employ a few embroidery stitches to create a repeated pattern around neck, sleeve, and even hem, if you so desire. Small glass beads as an accent are also very nice. Glass "gems" that are sewn on are also appropriate. There is a great guy who sells these, but has no mail-order thing set up. If you plan to go to Pennsic next summer, however, he's always there.