Investing in the stadium is cruicial but is not that important early on in the game.
Thats the first thing a manager should do - I sold out 18.000 seats in DIV III, that gave me a huge advantage when I finally moved up.
With a new team he wont be able to compete in DIV III anyway, so it is better to get in a position where you can stockpile money for a season and wait for a good moment (usually the offseason is the best time) to purchase players to get a competitive team for the next season.