How to go about finding a brokerage that's right for you

Investors who haven't already climbed aboard the Great Bull Market of 1982-83 may not only have trouble finding the best stocks; some don't know how to find a good broker who can help them select those stocks.

Time was, this was about all a broker did: Advise customers on the best stocks and tell them when to buy or sell. Today, brokers deal in commodities, mutual funds, asset management accounts, futures, and tax shelters. Then there are the discount brokers, who simply take and execute orders, letting customers do their own research.

Many people get started with a broker because the broker has sent them an unsolicited letter or called them at work or home. If the potential customer is ready to start buying stocks, he may just go ahead and start making investments through that broker. If the relationship works, fine. Otherwise, many investors spend as much time looking for a good broker as they do researching a potentially ''hot'' stock.

One way many people find a broker is by asking friends, relatives, or co-workers whom they use and how happy they are with that broker.

If the investor does not know anyone using a broker - or anyone who is happy with his - he may simply walk into a brokerage office close to his home or work. It may be a branch office of a nationwide or regional firm or the only office of a small, independent broker.

If you go the ''walk in'' route, ask to speak to the office manager or some other senior person. He will ask about your investment goals, income, the amount you plan to invest, and the risk you are willing to take. Sometimes this person will handle the account himself. But more often he will assign a new customer to a ''broker of the day,'' usually a position that rotates among the office's younger brokers.

Depending on a person's income, investing habits, and goals, there is a wide variety of brokerages to choose from.

The biggest group is the ''department stores'' like Merrill Lynch & Co., Prudential-Bache Securities Inc., Dean Witter Reynolds Inc., Paine, Webber, Jackson & Curtis Inc., E. F. Hutton Inc., and Drexel Burnham Lambert. In most cases, these are nationwide firms, some with hundreds of offices around the country. Increasingly, they are becoming wide-ranging financial service centers. Besides stocks and bonds, many also offer credit cards, life insurance, mutual funds, checks, financial planning, and loans.

While the fees at these firms are fairly high and a new investor may be shuffled from one broker to another, they do have the advantage of extensive research departments. These departments have looked into the backgrounds of most any company that catches an investor's interest. The departments include securities analysts who make themselves almost as knowledgeable about the companies and industries they cover as the company executives.

For more thorough research, there are the ''specialty houses.'' While brokers at these firms can trade almost any stock, they stick to a single market. For example, John Nuveen and Lebenthal specialize in tax-exempt bonds; ContiCommodity trades commodities; and Gabriele, Hueglin & Cashman, a small New York firm, deals in a wide variety of bonds. If an investor wants to keep a portion of his portfolio in one of these or other markets, these firms offer deep expertise many department stores can't match.

But if an investor wants to do his own research, or simply wants to trade a stock he already knows about, he can go to a ''discounter,'' like Charles Schwab & Co., Fidelity/Source, Quick & Reilly, or StockCross. The commissions are about half of that paid to a full-service broker.

For the well heeled, there are the large firms like Oppenheimer, Sanford C. Bernstein, and Morgan Stanley. These are sometimes referred to as ''the Guccis.'' Like the department stores, they have excellent research analysts, though they tend to cover fewer industries and corporations. Some have offices in several major cities, while others have only one. But almost all of them are geared to wealthy individuals and institutions with six- or seven-figure portfolios.

Once an individual finds a firm, he should spend some time interviewing the broker. Ask him to provide a list of some investments to suit your particular interest, income, and risk tolerance.

Once the account is opened, it is a good idea to pay close attention to it. Keep your own record of all transactions, their dates, and the amounts. Check the monthly statement the broker sends out against this record. If there seems to be an error, notify the broker immediately.

If the account is not being handled to your satisfaction, do not hesitate to switch. Even people who are happy with their brokers often keep their ears open for word of another one who is doing a good job, just in case a quick replacement is needed.