You can enable the built in loop tools addon, that’d have a circle option - I don’t know if there’s an easy way to conform the selection to other shapes as well.
Loop tool is good but also
blender has a tool to make a set of verts as a circle
use object transform to circle
but in some case might not work for all verts location
Hi
Regarding aligning vertices or objects, if you do not need to follow the shape of a native object such as circle, cone or else, then you can use a bezier curve, parent the object or group to the bezier curve and use curve deform… or following the menu follow path and so on…
After your objects are aligned to the shape of the curve, you can modify the alignment by editing the curve …