When it comes to fabric choice, it’s less an exact science than getting to know what would work, and there’s a few ways to go about finding the perfect material. One method would be to look at real-life garments that are similar and what they are made out of. You don’t need to know the names of the fabrics, but look at weight, texture, and other qualities, and then go to a fabric store and find materials that have similar characteristics. This is a great way to learn, and you’ll really get a feel for what works and what doesn’t for certain items.
You can also look at the back of your pattern envelope for suggestions – it’ll tell you some fabric names, and you can then go to a fabric store, find materials with those names, and see what they look and feel like. This is another good way to quickly learn, and can be a great starting point when overwhelmed, but keep in mind that the perfect fabric may not be suggested on the envelope because they’re just that: suggestions. (and suggestions assuming real-life garments, in most cases!)
Once you get a bit more advanced with fabrics, you can look at the garment and the world it comes from and ask yourself what materials would work there. For this garment, it appears to be something grungy and heavily weathered, and the garment is realistic in appearance, so something with a realistic texture (so not something super flat looking) and that can withstand your weathering would be best. Also look at where the character wears this – is the world one with mostly natural materials? What does the character do in this garment? This can help you narrow down your options once you have a few.
That said, here are my suggestions of things to look at.
The first fabric I would look at is a faux suede. The coat appears to be lined in fur, and it would make sense that the outside of the jacket in-universe is the backside of the fur. The suede would also keep the animal-based look uniform, and create a nice texture. Make sure to pay extra attention to pattern placement with a material like this, so that the nap of the suede is in a consistent direction once sewn.
Faux leather would be another, similar option, for similar reasons, though is more difficult to sew and a heavier material. Be sure to invest in a non-stick/Teflon foot for your sewing machine if you go this route.
If you want something that is suitable but not suede- or leather-like in appearance, there are many fabrics in the suitings and bottomweights category that would work for this. Look for something like a medium-weight twill with a high cotton or other natural fiber content, or something like a denim (which is a type of twill). A melton might also be good, though pricey. I wouldn’t recommend anything as soft as a gabardine.
Whatever you choose, it needs to be able to handle the weathering you are planning on doing, so get a swatch or buy a small amount and try any sort of painting, ripping, abrading, etc. you are planning on doing, and see how the fabric reacts.
I hope that helps! Good luck :]