Create the league, make sure you are in Commissioner mode. Go to the Game dropdown menu, then Game Setup, then League Setup. Scroll down to Release All Players/Clear Rosters and select it. Go to the Free Agent Screen and click Delete All Free Agents. Go back to League Setup and click Fill Teams With Fictional Players.
That'll give you your fictional league. I can't promise budgets will stay intact with their MLB counterparts because I've never tried it.
And I was resisting the urge to go all Al Swearengen on this post, you hooplehead.