German Twisted (or Old Norwegian) cast-on is my preferred method when working corrugated ribbing (see my post about corrugated ribbing). It is based on the long-tail method but involves an extra twist in the long-tail yarn (held around the thumb) to create a deeper and firmer cast-on edge. There are various online tutorials which explain this method. One of my favourites is by Lucy Neatby and can be found here. Another video, by Drops, can be found here.
Channel Island cast-on gives a decorative edge with little bumps as shown below.
There are several online tutorials, of which I have picked out one by Ysolda Teague here. In some versions of this cast-on knitters use an initial slip knot in addition to the decorative cast-on stitches which can be incorporated into the knitting by knitting it together with the next stitch (alternatively it can be removed from the needles and ignored and then undone before weaving in the ends). In Ysolda’s version there is no initial slip knot.
I searched around for a matching bind-off method and my favourite (shown below) can be found, with a helpful video, on the Knit Purl Hunter blog here.
The Channel Island cast-on and bind-off are used in my Murano Cowl pictured below.