The one thing we know for certain is that holding large amounts of cash isn't ideal - inflation tax will eat away at your wealth.
It's understandable that you're hesitant to put all your wealth in common stock. The S&P 500's price/earnings is 18.7 right now - a little high by historical standards. But consider that the S&P 500 has given a CAGR of approximately 10% (not inflation-adjusted) since 1970. If you don't time the market correctly, you could miss out on considerable growth.
So it's probably best to invest at least a portion of your wealth in common stocks, and just accept the risk of short-term losses. You'll likely come out ahead in the long run, compared to an investor who tries to time the market and ends up maintaining cash positions for too long.
If you really don't have faith in US equities, you could look at other markets, but you'll find similar P/Es in Europe and Japan. You could try an emerging market fund like VEMAX if you have the risk tolerance.
You can consider other asset classes like bonds, real estate and precious metals, but historically none have matched the long term returns of stocks. I would use them for diversification, but not as the primary growth driver.