The last couple of times I replaced the kind with the finish ring, I
got ones that are "self finishing." They simply set in the opening. Had
a nice big flange, and you set it in caulking that came with the sink.
Then, run a bead around the edge and wipe it to a nice contour. Took
more time to take the old one out than anything else. New ones were
ceramic, versus the old cast iron and enamel style.