Each person's answer to this question will be different. I own individual stocks because I like searching for undervalued companies, but as the market has risen, I've reduced some positions, and let more cash build up than usual. I'm not overly worried about a pullback because most of my stocks pay dividends between 2% and 8%, but I want to have some cash on hand in case either individual stocks or the market in general seriously retraces. FWIW, Buffet and Munger do the same thing.
If I suddenly received a large sum of new money, and I wasn't already a long-time investor with a lot of experience and knowledge, I'd take a while to study all of the various investment alternatives. The market has risen for nine years without a serious pullback, and the low interest rates may have artificially created a new bubble in the market. This has happened several times over the last two decades. When the high-tech bubble burst, everyone rushed into housing. People decided to put their money into something physically tangible that they thought would retain its value. The shift into housing created a different kind of bubble, and after that bubble burst, money shifted into the stock market and foreclosures. Many serious investors now suspect that the market is once again exhibiting "irrational exuberance," and they're either hedging their bets or reducing their exposure. If I decided to put money into an index fund, I'd "layer" my way in. IOW, I'd establish a modest position, and then wait before adding to that position. In the same way, if I decided to buy some CD's, I would only buy 12 month CD's, and wait to buy more every six months or so. That's because the Fed is raising interest rates, and CD rates usually rise in tandem.
Someone who thinks like an investor is always looking for something that appears to be seriously undervalued, and although a few (very few) individual stocks may be seriously undervalued at this time, the market in general is not. Whether it's fairly valued or over-valued cannot be known until later, but I don't know anyone (including many successful investors) who thinks that its undervalued. Just my two cents.