Amazon.com Inc. unveiled Monday its first small-format grocery store, Amazon Go, one of at least three brick-and-mortar formats the online retail giant is exploring as it makes a play for an area of shopping that remains stubbornly in-store.

Two of the other store formats Amazon is considering are bigger than the convenience-style Go store, according to people familiar with the matter. In November, Amazon’s technology team approved a proposal to open large, multifunction stores with curbside pickup capability, clearing the...