BARBER B. CONABLE is a sterling choice to run the World Bank. President Reagan's decision promises well both for the bank as an institution and for the American policies that increasingly depend on it. The United States wants to draw the World Bank more deeply into the international efforts to deal with the Latin countries' heavy debts. Mr. Conable will bring to the bank a soft-spoken manner, a strong intellect and great political skill.

The most important, and most onerous, responsibility confronting the next president of the bank will be to induce Congress to put up more money for it. Mr. Conable could hardly be better suited for this campaign of persuasion. As a congressman for 20 years he was one of his party's authorities on economic policy, respected even by those who disagreed with his practical and temperate kind of conservatism. A lot depends on success in winning greater congressional support for the bank. It is a cooperative enterprise in which the United States joins 148 other countries in managing it, and contributes about one-fifth of the capital. But the American contribution sets the scale for the whole operation and, if it is to do the work that the United States now has in mind, it will need more money in a year or two.

The outgoing president of the bank, A. W. Clausen, was greatly handicapped by the suspicions of the bank, and the hostility toward it, that the Reagan administration showed in its first years in office. All that changed a year ago when James A. Baker arrived at the Treasury Department and saw in the bank a potential ally. But the administration's earlier attitudes continue to live on in Congress, and Mr. Conable is going to have to change a lot of minds there. One way to do it is to point out that Latin America has been one of this contry's best markets abroad, but Latins can buy American exports only when their own economies are flourishing.

The second most important part of Mr. Conable's job will be the internal management of the bank. In recent years its lending procedures have been shifting, and it has begun to tie its loans more directly to changes that it considers necessary in borrowing countries' economic policies. Mr. Clausen is entitled to a bit more credit here than he's received. But the bank needs to go farther in that direction. Its experience suggests that poor countries get richer most rapidly when they open their economies to trade. But among countries with long traditions of half-closed markets, highly protected and subsidized, there's still a lot of persuading to be done. That's where the World Bank can be highly effective -- more effective, usually, than the United States.

Mr. Conable is stepping into an extraordinarily difficult job. But it is becoming an extraordinarily influential job as well.