The acronym MiLB is acceptable in all references to Minor League Baseball.

Do not capitalize related terms that do not include the full title: minor leagues, minor leaguer, the minors

The various levels of the minor leagues are spelled out and hyphenated:

Triple-A
Double-A
Single-A
Rookie

In MiLB-centered contexts (such as game stories), use the team name, e.g. Binghamton Rumble Ponies; Salt Lake Bees, etc.

In MLB-centered contexts (such as roster moves), use the level and the home city, e.g. Double-A Binghamton; Triple-A Salt Lake