If you play purely historical, you won't have enough players to support a minor league until 1910 or so. Then, you can probably support AAA and AA ball. It probably isn't until after 1925 or so that you can go deeper than that. You can dynamically change your league structure as you go along. That is, play with a reserve roster until 1910 and then add minor leagues in the preseason. Then add more leagues as you decide you have sufficient players to support it.
Note - I've always had to do the 'Let the AI set up all leagues, rosters and lineups' (whatever that button's official name is
) to get my players from the reserve roster onto the minor league teams when I do the changeover. The AI controlled teams do it automatically, so no worries with them.
If you play historical plus fictional, teams can still starve of players if the number of years served before a minor leaguer can go free agent is short. The AI never seems real interested in re-signing minor league free agents. Years of service before becoming a free agent is a pick you can set at league creation and can be changed during the preseason while in commissioner mode.
Normally what I do (assuming the use of fictional players) is make sure my lowest minor league has a large roster size compared to the others (say, 25 man rosters for AAA through SSA and the rookie league has a roster of 40). Then every year after spring training, when the Major League roster size goes back to 25, I go to commissioner mode and go to every team and fill their rookie league team with fictional players.
The other option I haven't really played with is high school and college feeder leagues, so can't tell you much about that.