Picking a broker who's tuned in to your needs

Maybe one of their letters landed in your mailbox recently.

Many stock brokerage firms -- some backed by new merger partners in retailing , credit cards, and insurance -- have taken to the mails to find new customers. Using mailing lists of ''targeted'' customers, the firms are telling people about their new services.

The industry has moved a long way from the days when a broker advised customers on buying and selling just stocks, earning a tidy commission. Now, brokers deal in such investments as commodities, money market funds, puts and calls, futures, limited partnerships, and real estate tax shelters. At many discount firms, where customers do their own research and use the broker simply to execute trades, commissions are much thinner.

If you receive one of these letters, or if the recent rise in the Dow Jones index has piqued your interest, you may decide it's a good time to jump into the market. But first it may be wise to shop around for the best stockbroker.

Many people find brokers through references from friends and relatives. If you and the person giving the reference have similar finances and similar investment goals, this can be a good way to go. It gives you more trust in the broker and keeps you from being assigned a broker, who may be competent but also new in the business.

Others, however, don't know anybody who knows a broker and are likely to walk into the nearest branch office of a major brokerage firm. If you do this, it is probably best to start with the office manager. Either the manager or the ''customer service representative'' will discuss your investment objectives, industries you are interested in, and how much you plan to invest.

In some instances the manager or service representative will handle the account. But more often he or she will refer you to a ''broker of the day.'' This is often a rotating position among the office's younger brokers.

The variety of new products and services being sold by brokerage firms means customers may not deal with the same individual broker for every transaction. Customers with the same person handling their accounts most of the time may often work with one of the firm's specialists. This specialist might handle specific stocks and mutual funds, for example, or will be an expert in tax shelters.

If you do not choose one of the large ''department store'' nationwide chains -- the Paine Webbers, Merrill Lynches, and Dean Witters of the world -- which provide complete research services, the type of broker you select will often depend on the industry in which you choose to invest. There are a number of specialty houses and regional firms that have developed a strong background in a few specific industries, companies, or geographic regions.

Many cities have a local or regional society of securities analysts which can provide a list of specialized firms in their area. Local and regional stock exchanges can also provide lists of their member firms.

Once you select a firm, find a broker who understands your needs and can react quickly to market trends. You might ask prospective brokers if they will provide a list of some investments to suit your income and risk level.

After you choose a broker, if you sense that he or she is not putting your money in the right investments or misses trends, don't be afraid to make a fast switch. In fact, you may want to keep a list of alternative brokers handy.

Once you have opened an account, keep an accurate record of all transactions, says Jeff McCord, a spokesman for the Securities Investor Protection Corporation , an agency established by Congress to insure customers from failing firms. ''Carefully check your monthly statement against your record of purchases and sales,'' he says. ''If there is an error, don't be afraid to notify your broker.''

If you don't get satisfaction, Mr. McCord adds, talk to the office manager or write a letter to the firm's head office. Letters to the the stock exchanges where the brokerage trades may also help.