Here are some of the players who may take the field in 1988: GEORGE BUSH. The man with what may be the longest resume in Washington, Mr. Bush has held a wide range of key jobs. Born in Milton, Mass., he graduated from Phillips Academy in Andover, and at age 18 became the youngest commissioned pilot in the Navy at that time. During World War II, he won the Distinguished Flying Cross.
Bush later co-founded an offshore-oil-drilling company in Texas. In 1966 he was elected to the US House. He later served as United States ambassador to the United Nations, chairman of the Republican Party, chief of the US Liaison Office in China, and director of the central intelligence, then vice-president.
JACK KEMP. The congressman isn't officially running for the nomination, but an aide concedes that Mr. Kemp these days ''sleeps with one eye open.'' Born in Los Angeles, Kemp graduated from Occidental College in 1957 with a BA degree. For a few years he played professional football, winning the most valuable player award in the American Football League in 1965.
As a seven-term member of Congress from western New York, Kemp is best known for his tax-cut legislation, which included ''indexing,'' a provision to protect taxpayers from automatic tax hikes caused by inflation. He is the author of ''An American Renaissance: A Strategy for the 1980s.'' He is highly popular among Republicans from coast to coast, in part because of his frequent appearances on behalf of GOP candidates.
HOWARD BAKER. Senator Baker's father and mother both served in the US House, and his father-in-law was Sen. Everett Dirksen of Illinois. Baker attended the University of the South and Tulane University, and received a law degree at the University of Tennessee. He served for three years in the US Navy during World War II, including a brief tour aboard a PT boat as a lieutenant junior grade in the South Pacific.
Baker was the first Republican senator elected from Tennessee in modern times. Besides his role as majority leader, he also gained attention as vice-chairman of the Senate Watergate committee. He is quitting his Senate post in 1985 - a move widely assumed to presage a full-fledged run for the White House.
ELIZABETH HANFORD DOLE. One of the most prominent women in the Republican Party, Mrs. Dole could very well wind up on just about everyone's list of potential vice-presidents in '88. She is also mentioned, however, as a presidential possibility in her own right. Dole, born in Salisbury, N.C., graduated with distinction in political science from Duke University. She later received a law degree from Harvard, as well as a master's degree in education and government.
Dole has held a number of government posts, including federal trade commissioner, deputy special assistant to the president, and staff assistant to the assistant secretary of Health, Education, and Welfare. On the Reagan staff, she served as assistant for public liaison prior to her swearing in as secretary of transportation on Feb. 7, 1983.
ROBERT DOLE. Political scientist Tom Cronin of Colorado College suggests a Dole & Dole team might be just the ticket for Republicans in '88. Senator Dole, of course, would like the first Dole in Dole & Dole to be him. The senator, born in Russell, Kan., became known nationwide after President Ford picked him as his running mate in 1976. His 1980 presidential bid ended early in the primary season.
Dole won a reputation for courage during World War II, when he was wounded in Italy. He spent more than three years in hospitals during his recuperation. He later received a law degree from Washburn University in Topeka, and also attended the University of Kansas at Lawrence and the University of Arizona. His political career began as a student, when he was elected to the Kansas Legislature. Later, after serving as a county prosecuting attorney, he was elected to the US House and then the Senate, where he heads the Finance Committee.
The field may include others. Among those mentioned: Sen. Richard G. Lugar of Indiana, who sits on three committees - Agriculture, Foreign Relations, and Intelligence; Sen. Jesse Helms, the New Right leader from North Carolina who is currently engaged in a bitter reelection battle; Lewis E. Lehrman of New York, founder of the Rite-Aid drugstore chain and a staunch Reagan supporter; and Gov. Pierre S. du Pont IV of Delaware.