year two for players who do all right.
Double A - It's rare for a player to start at double A and most players here have been in their club's system for a year or two. There are some veterans around who have been playing minor league ball for a few years and likely aren't going to make it past this level.
Triple A - This level is a mix of young guys who are close to the big leagues, old guys looking for new life and the so called AAAA players, guys who might get a short callup but are likely to spend the rest of their careers bouncing around AAA farm clubs.
Winter League ball - This is a place where guys can get extra work. It's most oftenthey finally start making the money they dreamed of and can play baseball at the highest level. 

It's a long road to get from the draft to the major leagues, excellent players often shortcut one or many levels of their team's farm system, but most players play for at least part of one season in the minor leagues (the last player to go straight to the bigs from the draft was Mike Leake in Cincinnati a couple of years ago)

