Another consideration is the curb appeal. What style of house is it? Is it an old house? If so, do you care if it is "historically accurate"?

How deep are the existing footings on the crumbling concrete stoop? Our old footings, thanks to a 4 ft frost line, were that deep. Removing the step was a jack hammer project.

Thanks for the replies! (I posted this over on "porches and decks" weeks ago and got none at all.)

Curb appeal is important, although I think either would look OK. Bluestone would definitely look better, but not if it's massively more complicated and expensive. The house itself is a 1950's bland ranch, which had been skewed (bad) "colonial" by a P.O. and we're reversing that. We live in a coastal Maine town and our reno is coastal/cottage with vaguely Craftsman accents to speak to the long low silouette and deep eave overhangs, as well as to the interior reno we're just finishing, which shares Craftsman attributes such as open living space, bringing the outdoors in, and lots of natural materials like slate, cherry, and other wood and stone. The exterior (currently) is structural colored cement block that looks like brick from a distance but isn't really, plus white vinyl from a P.O.'s early 90's addition. We'll be removing the vinyl and replacing with Kennebunker cedar shingles (oil-dipped in a natural grey-beige that looks like weathered cedar) and painting all the masonry in a similar grey-beige color. Side door is varnished fir, craftsman style. Cedar deck out back is long, low, sort of Asian. Garage will have cedar arbor/pergola overhangs on the garage doors. Landscaping includes cedar trellises, japanese maples, ornamental grasses, textured plantings, bluestone and slate.

The side porch (which we're also rebuilding) will be wood framed with Trex or cedar decking and simple square columns.

The front door is rarely used so it's mainly for curb appeal. There will be a flagstone path, fairly informal, just set into the grass, leading to it. It would look best in bluestone, but the framed wood would probably work as well.

I'm not sure how deep the existing steps are. It appears to be one solid mass of concrete and brick and stone. There used to be a major drainage issue in the front (since corrected) and they steps sank into the dirt over time. I don't know how deep they are. They SHOULD, of course, be 4 feet deep, but who knows. Yes, I expect it's a jackhammer project to remove them. So, theoretically, if we did wood, we could just build it all bigger than the existing mess, and leave that mess in place beneath the new porch (which will be higher anyway.) and that would probably be the easiest thing to do.

If we go with masonry, can we somehow go over the existing mess, or would we need to remove it all? What's the procedure for building and filling such a thing?

Existing steps (note that the "brick" cement block will be painted, and the door stripped and varnished with a new wood storm door. Landscape shrubs have been replaced with smaller ones):

I agree with staceyneil. Moreover, I agree with you ideas. Thanks!!

If the existing stoop has been stable since the drainage was rectified, and if you're going to keep the existing size and shape, covering what you have with a bluestone veneer would be the easiest, fastest, and least expensive.