The people who write the indices. Some are flakey and narrow, like the various Dow indices, now kept around for (dubious) historical comparisons and as headline fodder.

Some are broader and so slightly less dubious (S&P 500), or the larger n of the Wilshire 5000. Some aim for a different kind of breadth (e.g. MSCI).

All suffer from various epistemological problems (inclusion is largely on various market characteristics, e.g. mkt cap, volatility, etc), not to mention management challenges: e.g. ones like the dow are notoriously subject to weighting problems, not to mention splits; companies can change sector or of course merge or go out of business. So do you rebalance your index or not and by what criteria?

So you can pick what ever index floats your boat. Typically people pick very broad ones in the hope of an upward slope with minimal volatility. Black-Sholes would say that volatility is your friend but it hardly is for any normal investor.

The general idea is that you just want to have diverse companies whose profits and losses are uncorrelated. Since the market in general goes up you won't be hurt if say, Apple takes a nosedive because your small investment in Boeing makes up for it. A common approach is an S&P 500 index fund which invests in the 500 largest U.S Companies in the stock market. I wouldn't actually recommend only investing in index funds though, personally my retirement investment is a mixture of large capital index funds, small capital index funds, foreign index funds, and U.S Bonds. Talk to a financial planner (preferably a Certified Financial Planner IMO but I'm biased since I have a relative who is one) and make sure they have a fiduciary duty to you.