George Bush put the final touches on his Republican presidential campaign strategy late Tuesday with the selection of Sen. Dan Quayle of Indiana as his running mate.

The selection of Quayle - one of the best-kept secrets of the GOP National Convention in New Orleans - tells the country something about the kind of campaign Bush will run.Clearly, it will be a hard-hitting campaign centered on criticizing Democratic nominee Michael Dukakis for being more liberal than the American mainstream.

By opting for a running mate as comparatively unknown as Quayle, Bush is forgoing the big boost that could have been given the GOP ticket had he chosen to share it with some more prominent and experienced figure.

But Quayle likely won't hurt it, either.

Moreover, by picking as staunch a conservative as Quayle, Bush is doing much more than just providing a sop to the right wing of the Republican Party - which once considered Bush too moderate for its taste.

Rather, Bush in effect served notice that he and Quayle can be expected to lambaste the liberal Dukakis and his fairly conservative Democratic running mate Lloyd Bentsen for being so far apart ideologically. Such an attack would have been untenable if the Republicans had aped the Democrats' exercise in ticket-balancing.

Geographically, the selection of Quayle is no act of ticket-balancing either. His home state, Indiana, could be expected to go Republican with or without him sharing the top of the ticket.

Frankly, the selection of Quayle is somewhat surprising because of his comparative youth, 41, and relative inexperience - two undistinguished terms in the House of Representatives and two in the Senate.

Yet, with choice assignments on the Senate Budget, Armed Services, Labor and Human Resources committees, Quayle has accomplished more than anyone expected when he first arrived in the Senate eight years ago. Among other things, he has spearheaded efforts to get private business rather than local governments involved in job training and introduced a sweeping tax simplification plan.

Quayle stalwartly supported President Reagan's economic program, but as time went on he became concerned about growing deficits and backed efforts to force deficit cuts.

On the Armed Services Committee, Quayle was skeptical about the size of military spending increases sought by former Defense Secretary Caspar Weinberger and in 1985 he proposed changes in defense procurement to promote more competition among contractors. Yet he is an aggressive supporter of President Reagan's Star Wars program.

Quayle, known for his cheerful temperament and a slight resemblance to actor Robert Redford, has concentrated on economics and foreign policy in the Senate. Before entering politics, he served briefly as associate publisher of his family's newspaper, the Huntington Herald Press.

In any event, the timing of the announcement of Quayle's selection tells something about Bush's political acumen. If the announcement had been held until the last day of the New Orleans convention, continued speculation about the identity of the vice presidential nominee could have deflected attention from Bush's acceptance speech - the biggest speech of his political life.

One final point: It has become fashionable to belittle the office of vice president and, consequently, to consider the selection of a running mate to be of little significance. But keep in mind that plenty of people more experienced and accomplished than Dan Quayle were more than willing to share the ticket with George Bush. For all its problems and comparative lack of prestige, not many people turn down the vice presidency - and wisely so.