I would say that "classico" can be translated simply with "classic". "A Classic", in literature, cinema or music, is something that is outstanding in its field; of a recognised value and also well known. And moreover a classic is usually considered 'without time'.
"Film classici" are Amarcord, Breakfast at Tiffany's, Nuovo Cinema Paradiso, but also Go With the Wind and The Battleship Potemkin, in my view. You can like them or not, but you cannot ignore them.
The point is one thing (suspense, giallo) refers to the genre; the other (classico) refers, like aglaja said, to it being a must-not-miss anyone who claims to like movies has to deal with. A movie can (obviously) be both a classico and a giallo, they're not mutually exclusive