For greyhounds, whippets, Italian greyhounds, we usually use fleece -- single layer for indoors, double layer for long walks outdoors when it's very cold. Most common is a vest-like pattern (no legs). Legs do help keep it from sliding around as much but some dogs find them uncomfortable.
The one downside to fleece is static! Dryer sheets are your friend. If the dryer sheet chemicals bother the dog, you get less static with cotton flannel or all-cotton knit.
Hope your pup is well and that you have fun making some coats!