"Why buy it through a broker while Vanguard does not charge the commission?"
Only reason I can come up with is that it may be easier to manage your holdings if they are all in one account. That said, while all of my equities are with Fidelity, I own VTSAX directly with Vanguard.
Kudos to you for considering this fund (or Vanguard's Total Market Fund). This fund is an excellent foundation for any investor and you may find over time that an index fund outperforms your other holdings; again, over time. Very tax efficient to boot. Periodically add and reinvest your dividends too!