A lovely rectangular wrap, floaty & light lace:
I like rectangular shawls, provided the size is generous. I see a lot of "shawlettes" on the hand knitting sites, very small small shawls. Those aren't for me - I like the larger, drapier lavish ones, like this beauty.
One thing to appreciate about airy handknit shawls is the practice of very firm blocking, which gives the silky, sheer, lace-highlighting result. This is typically done by pinning the shawl out wet.
You could "kill" the knitting with a steamer, that is, steam it hard and flat until there is no elasticity. This results in a sheer, silky hand like the picture, at least in most fibers. If you decide to "kill" a machine knit shawl, "kill" a sample first so you know what you're going to get.
At knit club last month, we "killed" some of that bubble wrap stitch. It was amazingly lacy and slinky steamed hard!
You could make a rectangular knit shawl like this on the knitting machine and then knit an edging using Enchanted Edgings patterns. However, you do have the issue of how to go around the corners; one way would be to gather the edging for a bit of a ruffle. Another solution would be to short-row a miter using a piece of ravel cord. To make a miter work, you'd need to plan the project so it is the proper number of rows and the edging ends at an end of the pattern repeat. Another way to go would be to make some tucks just in the corner where the seam is so that there will be enough edging to go around the angle.