As ChrisInEdmonton describes, shorting has an asymmetric risk/reward ratio. And put options have a time cost, if you think the market is overvalued and buy lots of puts, but they expire before the market finally corrects, you can lose your entire investment.
Betting on market timing of any kind is extremely difficult to do, some would argue it's impossible. "The market can remain irrational longer than you can remain solvent" is a favorite wall street trader saying. Instead of playing a game that's difficult to win, the better option is to play one you can win. That's to learn how to value individual investments well and accumulate cash until you can find investments that are under-valued to invest in.
The best way to learn to value investments is to read Graham and Buffett. "The Intelligent Investor" is a good starting point, and you can read all of Buffett's investor letters for the last 30 years + for free on the Berkshire Hathaway web site. Finally the textbook on valuing stocks and other investments is "Securities Analysis" the 6th edition is only version to get, it was updated with Buffett and other leading value investors oversight.
A basic overview of valuing investments is that every investment has an "intrinsic value" consisting of it's future cash flows, discounted for the time it takes to receive them. The skill is being able to estimate how likely those cash flows are to happen.
a) Is it a good business? Does it have a moat, i.e. barriers that make it hard for competitors to duplicate it?
b) Will management invest or distribute those cash flows wisely?
Then your strategy is to not even worry about the market, spend your time looking at individual stocks and investments and wait until some come along that's well undervalued. That may be during a market correction, or it may be tomorrow. And it's not just good enough to intelligently value your investments, you also have to have psychological fortitude to not panic and to think for yourself. Buffett describes it best.
Ben Graham, my friend and teacher, long ago described the mental attitude toward market fluctuations that I believe to be most conducive to investment success. He said that you should imagine market quotations as coming from a remarkably accommodating fellow named Mr. Market who is your partner in a private business. Without fail, Mr. Market appears daily and names a price at which he will either buy your interest or sell you his.
Even though the business that the two of you own may have economic characteristics that are stable, Mr. Market’s quotations will be anything but. For, sad to say, the poor fellow has incurable emotional problems. At times he feels euphoric and can see only the favorable factors affecting the business. When in that mood, he names a very high buy-sell price because he fears that you will snap up his interest and rob him of imminent gains. At other times he is depressed and can see nothing but trouble ahead for both the business and the world. On these occasions he will name a very low price, since he is terrified that you will unload your interest on him.
Mr. Market has another endearing characteristic: He doesn’t mind being ignored. If his quotation is uninteresting to you today, he will be back with a new one tomorrow. Transactions are strictly at your option. Under these conditions, the more manic-depressive his behavior, the better for you.
But, like Cinderella at the ball, you must heed one warning or everything will turn into pumpkins and mice: Mr. Market is there to serve you, not to guide you. It is his pocketbook, not his wisdom, that you will find useful. If he shows up some day in a particularly foolish mood, you are free to ignore him or to take advantage of him, but it will be disastrous if you fall under his influence. Indeed, if you aren’t certain that you understand and can value your business far better than Mr. Market, you don’t belong in the game.
Lastly learning to value investments isn't just useful in the stock market, they are applicable to investing in any investment such as bonds, real estate, and even buying your home or running a business.