Modeling a low-poly crater in Blender Quick disclaimer: I'm relatively new to Blender, and so I apologize in advance for my ignorance.



"What is the best way to approach modeling a Low-Poly crater in Blender?"

Here's an example of a crater on Earth. I'd like to use the low-poly art style and make different variants of craters similar to this.





I've tried two approaches so far:


Bézier curve: I tried using the Bézier curve tool to outline a crater from the top view. I then sub-divided the ground and crater into triangles, and then randomized the materials assigned to each of the faces. This was very time-consuming, and the end result feels very unnatural.

Sculpting: I then tried sculpting for the first time. While it looks nothing like it, I think I'm on the right track, but I'm clueless as to how to achieve the desired result. The terrain (when imported into Unity) feels a lot more natural, but I cannot seem to get the sharp ridge on the crater walls right.



Are there any better means of achieving this result? Any help would be much appreciated.

Thanks.
Lazy tutorial ... 


download (export) terrain high-map from here https://tangrams.github.io


Link is set directly to your Barringer crater. Exported image seems like just a screenshot saved in 8-bit, that makes it lately a bit blocky for displacement (16 or 32-bit would be better for smooth result), but since your goal is low-poly, it's more than enough.




subdivide plane few times to make topology more dense, plus add Subdivide modifier to get grid even more dense to catch details





add Displacement modifier, assign downloaded high-map (greyscale image) as Texture, Strenght = 0.1





add Decimate modifier, Ratio = 0.01








Landing on Surface


add Cylinder and Boolean-Intersect it from crater to get circular shape





go to Weight Paint mode and click in center from top view to get gradient





search for "Invert" to get red color of gradient from center on edge





add any "land" object (surface you want to follow) 
use snap tool to bring center of crater object to surface (with "Align Rotation to Target")





add to the crater object Shrinkwrap modifier and choose a Vertex Group (in this case called "Group" generated by Weight Paint mode automatically)





Works for concave and convex shapes as well ...




In this particular case (crater) probably could be enough to duplicate and rotate / scale object, that will brings illusion of crater variations without needs to make them unique, but you can sculpt a bit each of them to make more variations.