I'm guessing you are looking to collect a current baseball player but seeing you are a Twins fan, I'd look into collecting one of their older legends like Harmon Killebrew or Rod Carew. The challenge would obviously be in their early cards but you would not have to worry about chasing cards I refer to as "manufactured scarcity" or numerous variations of the same card in newer issues. Certainly some of their cards would be scarce like Carew's 1967 high # RC but it is not a purposely short printed card. Players like these would also give you a reasonable amount of cards to chase not to mention you would not be making a risky investment by collecting a new prospect which is always dicey as so many of them fend up in the commons boxes.
Just my 2 cents while showing my preference for the older players.