President Reagan Tuesday picked a "tough-minded crime buster," former Pennsylvania Gov. Richard L. Thornburgh, to succeed Edwin Meese III as attorney general.

Thornburgh, a squeaky clean ex-prosecutor with a reputation for staying cool under fire, declined comment on the troubles of Meese, who has been dogged by questions about his ethics and who announced last week that he had been exonerated by a special prosecutor and would leave office Aug. 1.Thornburgh said, "I think it is important to look forward rather than back. I think what we will try to do is to carry out a full-bore effort in the law enforcement area."

Asked if he would have to look into investigations of Meese, Thornburgh at first declined to answer, then added, "My intention in this as in any areas is to follow the evidence wherever it may lead."

Meese could still face an internal department review of his actions.

Reagan, who appeared with Thornburgh in the White House briefing room, called Thornburgh "the ideal choice for attorney general.

"I urge the Senate to move quickly to confirm him as well as our other Justice Department nominees so they can roll up their sleeves and get to work enforcing the laws of the land."

Also awaiting Senate confirmation are the deputy attorney general, Harold Christensen; the No. 3 person in the department, Associate Attorney General Francis Keating, and the criminal division chief, Edward Dennis.

Christensen and Keating have been on the job since early June; Keating has been at work about a month longer. All were appointed on an acting basis by Reagan.

There appeared to be little opposition in the Senate to the Thornburgh nomination.