I can't speak for a Type A since I don't own one but for the ones I do which are a B1, C1 and C2 the B1 gives me the closest shaves of the 3.A nice soak and scrub with warm water and dish soap, followed by a polish worked wonders. Surprised me how nice it was underneath.
Fortunately, unlike my Type-A, this guy didn’t need to be tightened up. The modern blades fit snuggly without any movement.
I'd also add I can't tell a difference between how the C1 and C2 shaves. Unless you are collecting every B or C type, get the C2 which is the easiest to acquire and you'll be good to go for you Schick A,B,C's as far as different types of shaves each letter can do.