NEW YORK (CNN/Money) - What is a good way to invest about $10,000 right now? I won't need this for at least 10 years.

-- Eddie Perez, Pearland, Texas

Back in 1841 when a young man asked New York Tribune Editor Horace Greeley where the best opportunities were for an ambitious young man, Greeley famously advised him to "Go west, young man."

Actually, what he wrote was, "Do not lounge in the cities! There is room and health in the country, away from the crowds of idlers and imbeciles. Go west, before you are fitted for no life but that of the factory."

So what is my advice to someone more than a century and a half later who wants to know how to invest a tidy 10 grand over the long term? Let me put it this way: "Do not cower in CDs or bonds! There is room for healthier gains away from the crowds of wimps and fearmongers. Buy stocks, before you look back 10 years from now and realize that instead of hunkering down in fixed-income investments, you should have taken a prudent risk in equities."

Okay, so maybe my advice doesn't have Greeley's flair, and I doubt anyone will be repeating it in 2163. But I still believe that this is the best advice I can give to someone who's investing money for long-term goals today: Put the bulk of your stash in stocks.

Here's my reasoning. In terms of investor psychology, now is a terrific time for buying stocks. Why? Because our fellow investors hate them. That's right, fear is good when it comes to stock returns.

If you buy when everybody loves stocks -- as they did back in 1999 -- your upside is limited, simply because the herd has bid up prices so high that companies had virtually no chance to deliver profits large enough to justify their stock prices. (Which, by the way, probably has a lot to do with why so many companies committed outright fraud or stretched the envelope to make it appear they were meeting unrealistic expectations.)

But when investors loathe stocks, their expectations are low. That means companies are more likely to beat those expectations, and stock prices have more potential to run.

Another reason I like stocks now is that they're looking pretty damn cheap. Perhaps not screaming-bargain cheap, but attractive nonetheless. There are many ways to judge the value of stocks, but one measure I like is the Fed stock valuation model.

Basically, this model compares the yield of 10-year Treasury bonds with the earnings yield of stocks -- that is, the expected earnings for the Standard & Poor's 500 index over the next 12 months divided by the index's price.

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In effect, the model looks at stock earnings as if they were bond interest payments, and then compares those payments to the interest one would get by buying 10-year Treasury notes. The idea is that the 10-year Treasury yield and stocks' earnings yields should be pretty close to each other. If stocks' earning yield is higher, then stocks are probably a better buy. If the 10-year Treasury yield is higher, then it's the better deal.

Over the past few weeks, the earnings yield on the S&P 500 has been hovering in the 6 to 6.5 percent range. The yield on Treasuries, meanwhile, has been hovering just below 4 percent. That means that on the basis of this valuation model, stocks have been undervalued by anywhere from 25 to 40 percent relative to Treasury bonds. (If you'd like to calculate how undervalued the market is based on where you believe corporate profits will be in the next year, try Dr. Ed Yardeni's Stock Market Valuation Calculator.)

I admit there's plenty of room for error in the Fed stock valuation model. For one thing, analysts could be overestimating corporate earnings over the next year. But historically, this gauge has been a pretty good indication of stocks' future returns.

When stocks have been overvalued by 20 percent or more on this gauge, their returns over the next few years have been generally subpar. And when stocks have been undervalued by 20 percent or more, they have tended to generate above-average returns over the next few years.

So how should you follow my advice to buy stocks? That depends on how much research you're willing to do.

If you don't mind gathering lots of data at places like our Investor Research Center or other financial sites, and you have the analytic prowess to evaluate individual companies, then buy individual stocks. If, on the other hand, you'd prefer a professional money manager do the stock picking for you, then you're probably better off in mutual funds. You'll find no shortage of ways to screen for solid funds at our Fund Screener tool.

As for me, I take what I consider to be both the easy and the smart approach. I tend to stick to index funds -- funds that buy and hold the securities of a specific index. I don't believe there are that many managers out there who can consistently beat the indexes after deducting their costs, and I have even less faith in my ability to identify those managers in advance.

So I prefer the convenience and low cost of index funds, especially those tracking the broad U.S. stock market. For details on the index choices available and how to build a portfolio using index funds, click here.

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One more thing: notice I said above to put the "bulk" of your stash in stocks. I don't like making all-or-nothing bets. That's why I believe that, no matter how bullish you are on stocks, you should always make room in your portfolio for some bonds, and, for that matter, maybe even some CDs. For guidelines on how much to devote to bonds, click here.

By the way, the young man to whom Horace Greeley gave advice was a fellow named Josiah B. Grinnell. Grinnell did indeed go west, to Iowa, where he founded the town of Grinnell and donated land to a college now named for him, Grinnell College.

I can't guarantee you'll meet with comparable success in the stock market. But I think you'll do a lot better there than you would with the alternatives. Good luck.

Walter Updegrave is a senior editor at MONEY Magazine and is the author of "Investing for the Financially Challenged." He can be seen regularly Monday mornings at 8:40 am on CNNfn.