Evenhanded look at Joe McCarthy; The Life and Times of Joe McCarthy, by Thomas C. Reeves. New York: Stein & Day. 819 pp. $19.95.

There are three categories of readers who will be zestfully interested in ''The Life and Times of Joe McCarthy.''

There will be those who believed McCarthy could do no wrong.

There will be those who believed McCarthy could do nothing right.

There will be those who simply want to know what went on during the McCarthy period -- and why -- and who hope they can depend on Professor Reeves to give them an honest count.

They can. His book has been carefully and exhaustively researched and deserves the wide readership which I expect it will get.

Dr. Reeves, who is professor of history at the University of Wisconsin-Parkside, does not exonerate McCarthy from his reckless, meat-ax approach to anybody and everybody he deemed a Communist. At the same time, he does not fall into the pit of total condemnation, as did so many of the contemporary journalists who were writing about him so viciously at the time.

Dr. Reeves's work will not please the all-out enemies of McCarthy, who still abound in many places.

It will not please the uncritical admirers of McCarthy. There are still quite a few of those around. It is too fair and too evenhanded to satisfy them.

McCarthy was an ambivalent fellow. He allowed himself to be propelled into his anticommunist crusade by events. He had run out of effective issues in his campaign for the Senate. He ended up in Wheeling, W.Va., on a five-state fund-raising campaign and delivered a speech written by a newspaper friend of his. It was a speech proclaiming that the federal government was infested by card-carrying Communists and fellow travelers. He found he had hit pay dirt, and he kept it up from then on.

He would dramatically hold up a sheaf of papers and announce that ''I have here the names of Communists in the State Department.'' The papers were blank sheets. He never let these blank sheets out of his hands, and he never revealed the names.

A text of 675 pages (plus notes and bibliography) is a formidable challenge to any potential reader. My counsel is not to gulp it, but sip it. Choose those chapters that interest you most or which deal with events about which you know the least.

It seemed to me the most engrossing chapter in the whole book is the one that dealt with the famous Army-McCarthy hearings, which brought McCarthy's downfall as a person and as an anticommunist crusader. As a Washington correspondent, I covered much of these hearings, and I found the chapter more fascinating than anything else in the book.

Perhaps the most telling excoriation of McCarthy came from the gentlemanly and gracious Boston lawyer Joseph Welch who, in response to one of McCarthy's more disgraceful attacks on one of the witnesses at the hearing, cried in outrage: ''If it were in my power to forgive you for your reckless cruelty, I would do so. I like to think I am a gentleman, but your forgiveness will have to come from someone other than me. Have you no sense of decency, sir, at long last? Have you left no sense of decency?''

Senator McCarthy's greatest offense, his greatest crime, is that he made anticommunism a dirty word, and delivered a crushing blow to legitimate and constructive and needed anticommunism.

Dr. Reeves's ''Life and Times of Joe McCarthy'' is a valuable book.