So IMO decide on what you want the coat to be. One-coat-for-all-occasion or a "fun" piece? If you just only have a budget for 1, I wouldn't get the leopard one or the leather-looking one as they aren't versatile. My ranking would be 4, 3, 1, 2 for the following reasons.
The last one is the most basic, and hence you can wear as a topper to a professional outfit, to jeans-sweater casual. It can be your interview coat AND your going out coat AND your vacation coat. Navy, camel, black and white/cream are my go-to colors for building a "foundational wardobe" (1 coat, 3 nice blouses, 1 real leather belt, 1 pair business slacks, 1 pair casual pants, 1 suit, 2 skirts, 3 tees, 1 sweater, 3-4 casual/fancy dresses, 1 pair of work pumps, 1 pair of casual loafers, 1 pair sneakers).
Leopard is fun, same with bright red, for a coat, but it doesn't work with every outfit. If your underneath style is usually very simple (black/white/other neutrals) a leopard coat is great. Otherwise, I wouldn't get it.
Faux leather can look really cheap in person depending on the manufacturing so I would never get faux leather unless I can A. return it easily or B. examine it in person before purchasing. It could also rip easily.
Shearling hooded one is great if you don't need to look business-professional in it. I like that one a lot. I just picked the 4th one over it because the 4th one is more classic/less trendy.