How to Choose the Right Total Stock Market Index Fund

Vanguard Total Stock Market Index Fund, or ETF, or the Fidelity Total stock market index fund. Both of all three of these indices have over 4,000 stocks. This is what I'm looking for. So this is the fund, the index I want. What funds areETFs are available that follow that index? And then who is the fund sponsor? Is it a big company like a Fidelity or a Vanguard or Schwab or some of that?