I'm a sucker for the neatness of the square.

Yours do look very nice but don't forget there are 1000s of homes with laminate bench tops with cook tops sitting directly on them. Don't think that the sides of a BBQ get hotter than a wok burner. I do like your first pic, the more compact one. What would be the approx cost sans BBQ?

A lot of the time they build a core filled concrete block wall then construct another stone wall against it. The concrete block wall takes the job of retaining while the stone is for looks only. It does depend on what purpose the wall is performing. For example a retaining wall higher than 600mm (usually) needs engineering by a structural engineer which is easier to achieve with core filled concrete block on footings rather than just solid stone. You never mentioned the purpose of the wall which is a vital detail as there can be numerous ways to achieve similar outcomes.

Got my answer - non combustible material such as, natural stone - marble, granite or concrete etc.