If MLB is premier league what would be the comparison for Minor League? Championship?
It doesn't really work like that. Minor League teams, whilst having their own competition, are mainly feeders for MLB. There's no promotion/relegation.
There are now four main levels of Minor League. In descending order.... AAA, AA, A and Rookie. Historically there were more levels and many more Minor League teams than there are now.
Each MLB team normally has one AAA affiliate, one AA, two A and one Rookie.
Players on AAA teams are usually the first to be called up to the Majors if the need arises.
I find it fascinating to watch Minor League games and try to spot which players have potential to make it at the highest level.
For example, in June 2017 I attended three games at the Portland Sea Dogs (AA affiliate of the Boston Red Sox). They had a 20 year old 3rd Baseman called Rafael Devers. It was obvious to even my non-expert eye that he was far too good a player for that level, even though he was one of the youngest players. In July 2017, Devers was promoted to AAA Pawtucket and by the end of the same month he had made his Major League debut.
Last season Devers was the starting 3rd Baseman as the Red Sox won the World Series.
I've now been to 33 Minor League games on top of my 285 MLB