I have a ring of select vertices, with an actively selected vertex. I can tolerate ngons. How do I evenly reduce the vertex density without destroying geometry and without doing nearly any work?
First, use a checker deselect operation (on operator defaults). Then, dissolve vertices.
Okay, what if ngons are not tolerable to me? (This is a situation where the topology has bigger problems than ngons, but whatever.) I start as above. Then I give the mesh a subdivision modifier and apply it:
And, indeed, this pic shows us how we can step down vertex count manually, should we ever want to.
Or, is there a far better way I should approach this altogether?
Yes. The first thing that you should do is use fewer vertices. The only thing that makes it difficult to manually edit your mesh is the vertex count. Even if you find a way around that here, it will bite you elsewhere. One of the best bits of advice I've found for 3D modelling is, "Work from low detail to high detail." Here, for you, that means that if you need something circular, start with a circle of 8 verts, not 800. It is far easier to create more, smooth vertices via subdivision than it is to remove existing vertices; it is far easier to destroy smoothness than it is to create the smoothness that comes from low vertex counts. Here, there's a valid complaint that applying subdivision makes too many vertices-- but, that wouldn't be too many vertices, if we were starting with half as many vertices to begin with.
The second thing (and this ties into what I was saying, that this isn't going to be good topology anyways) is that, for a good model, your choice of how to connect your vertices depends on your shape. You shouldn't just make a bunch of concentric circles and then displace them to make a decent hill; you need to actually model the hill. A hill made out of a grid will be grid-like; a hill made out of concentric circles will be cone-like.
I said, if we need all quads, that we can just apply a subdivision modifier to turn this mesh (or any mesh!) into all quads. But all-quad is only a part of good topology. Our all-quad mesh is full of 5-poles and 3-poles. These poles are unavoidable for stepping down vertex counts. But where these are placed is part of good topology. On this flat circle? They're fine. Once we turn it into a hill? Who knows? It depends on the specific hill. So the all-quad version is just to satisfy people who are only starting to learn about topology (and isn't, in reality, any better than the ngon-version.) But we can't say what would actually be good topology without knowing which specific hill it will turn into.
