Well, it's both. Certainly I, playing a 6M Conn, fall in the Sonny Criss (Selmer BA), Arthur Blythe (Buescher True Tone with Berg(!)), Lou Donaldson (Selmer) range of sound.
Without a doubt, the design of an instrument pulls the player's tone a particular direction, but also the player's personal tendencies pull the "design tone" character of an instrument a particular direction. Compare Lester Young and Chu Berry, two guys playing Conn 10Ms and Link mouthpieces; or Ben Webster and John Coltrane, two guys playing Selmer saxophones with Link mouthpieces.
But the OP doesn't HAVE a personal sound yet. I think the best advice for someone just learning to play, is to get a middle of the road setup and to make sure the horn is in excellent playing condition.