Silk is the most common in surviving garments, but that doesn't mean it was the only choice (it just means they were more "valued" and saved). Many portraits look like taffeta, two extants are made from quilted satin (one, two), another is a watered silk, and I used a corded silk.
There is one portrait of a printed cotton and Barbara Johsons book of swatches shows a manchester cotton (small check). The Colonial Williamsburg Milliners used a similar pattern in silk, which the amazing Susan Parris used as inspiration for one of her dolls.
While other fabrics, like wool, don't have any references it doesn't mean they didn't exist. If you want a comfortable, easy, and warm fabric wool would qualify well.
It can be low or high neckline.
You can also decide how the jacket will attach to the waistcoat itself. I chose to make a separate waistcoat which the hood was attached to. The jacket simply pins to the front when wearing. Another option is to make the waistcoat fronts and have them attach at the shoulder and side seams. A final option is to make false fronts where the fashion fabric attaches to the jacket front seam. The lining encompasses both pieces. In the last two cases the jacket back is higher on the neck to meet the waistcoat neckline.
Cuff or Flounce. You can see both in the images above. I chose a cuff because my fabric had too much body for a flounce.
The bottom part of the sleeve is a very simple trapezoid that whips into the main sleeve. The seam is left open at the wrist for a few inches so it can be more fitted.
It's no different than a cloak hood in patterning. You can gather or pleat up the back (even put a bow on it, as Janea showed us). It pleats into the neck line.
I lined the main body with linen to just below the waist, as well as the sleeves. The lower sleeves and hood I did in a taffeta. You can also line the skirt with a fashion fabric.
Usually out of the same fabric, pleated or gathered. Although, I have seen a few portraits with contrast fabric or gauze.
They are all fairly heavily trimmed. Around the hood, down the front, around the hem, on cuffs or flounces, sleeve hem, and up the center of the waistcoat. You also see bows on the cuffs/flounces and center front on the low necklines.
There are many other details that you can find in examples/portraits which makes this garment so unusual and customized. The hem can dip in back or run straight, corner or curve in front. Wear it with a habit shirt, kerchief, or ruffles. The hair tends to be done up in a very fashionable manor, occasionally with a cap or bow. Granted, these are formal portraits and sitting with a fancy hairstyle is easier than traveling with it. There's even a slight variation to the Brunswick with a full length skirt called a Jesuit.