I have imported the image below as a plane, and am adding lots of vertices to the plane in preparation for dividing it into quads and triangles that are aligned with the contours of the mountain shown.

mountain on moon edited in blender

When going through tutorials, I recall it being said that one should avoid triangles whenever possible. Once I have created all the vertices and start connecting them, dividing up everything into spaces that make sense to stretch vertically and thus form the contours of the mountain, do I need to plan well to avoid triangles? These points are going to be pulled fairly far along the z axis, and then they will need to be proportionally edited and subsurfaced to get the soft shapes of its slopes correct. I wouldn't want patches to start misbehaving once I've gotten to that point. Are there general guidelines about this?

I'm no expert on mesh topology, but I do know that good topology (with nicely flowing edge loops and almost only quads) is important especially if you want to animate and deform your mesh, and less so in most other cases.

Some tools work better with quads than tris, such as the subdivision modifier which sometimes generates weird artefacts, especially when the mesh is irregular. EDIT: Rigging and skinning is also easier when you have a clean quad based topology with nice flowing edge loops.

In most other cases triangles will pose no problem (I might have forgotten a few other examples for issues, which others here might add, but there probably aren't that many). You can texture, shade, light, 3D print with ease even if your entire mesh is made of tris.

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