As I understand it these Indexes are baskets of assets that are securities. Does that make the Index itself a security? What about an index of commodities?
No, the indices are not securities. They are basically lists. The Dow Jones is a list of 30 companies, and the Standard & Poors 500 (as it says in the name) is a list of the 500 largest companies in the US. You can't invest in DJ or S&P 500 directly, since they are just lists, not securities.
There are several securities (index funds, ETFs) that track these indices by owning every equity on the list. They use different approaches to decide how much of each to own, which can affect performance. Investing in a fund like this will (usually) involve paying some fee to the fund manager. You could avoid that by investing in the underlying securities yourself (the companies on the lists), but that would involve a lot of management on your end, decisions about how to weight your holdings (and when and how to rebalance), and a lot of startup capital to buy all the necessary shares.
The S&P 500 and Dow Jones Industrial Average are not securities themselves, but rather they are indexes that track the performance of a group of securities. An index is a statistical measure of the performance of a group of securities, typically a stock market index such as the S&P 500 or Dow Jones Industrial Average. These indexes are created by companies such as Standard & Poor's and Dow Jones, and they use a specific methodology to select the securities that are included in the index and to calculate the index value.
An index of commodities, such as the Bloomberg Commodity Index, would work in a similar way, with the index tracking the performance of a group of commodity futures contracts. In this case, the individual futures contracts would be the securities, and the index itself would not be a security.