Israel's Prime Minister Menachem Begin is coming to town in an angry, feisty, frustrated frame of mind, according to officials who should know. The question even they can't answer is how much he will allow it to show.

At least some of the Reagan administration's most influential policymakers are increasingly in favor of bearing down hard on Begin if push comes to shove, as it very easily could. The question they can't answer is how far President Reagan, in his first meeting with the Israeli prime minister, is prepared to go.

All of which suggests that his meeting with Begin shapes up as by far the most unpredictable and portentous of any of the getting-to-know-you first encounters that Ronald Reagan has faced.

Consider how precariously the stage is set. What with one thing or another (the Israeli use of made-in-America warplanes to bomb Baghdad and downtown Beirut; the Begin government's obstruction, in American eyes, of West Bank "autonomy"), Israeli relations were already quite sufficiently strained. Now the proposed sale of American AWACS aircraft to Saudi Arabia has Reagan and Begin on a clear collision course.

American public support for Israel in general and Begin in particular has rarely been so low. That might be reason enough for Begin to exercise restraint.

But Begin apparently thinks that his best defense is a good offense. "He comes here believing he doesn't owe Reagan anything," says one informed Israeli. The Israeli prime minister believes, deep-down, that the administration not only wished secretly for his defeat in last June's Israeli election but worked for it by not helping push the Camp David process forward earlier this year when the "peace" issue was his most effective campaign talking point.

So Begin will arrive well armed with grievances of his own if the Americans want to rake over old unpleasantnesses. Mention of the hang-up on delivery of F16 fighters bought by Israeli will be met, I'm told, by sharp reminders that those planes were part of a firm quid pro quo for Israeli agreement on the second-stage withdrawal from the Sinai on Sept. 15.

If things get heavy, Begin will not hesitate to remind Reagan that his administration's agreement to "enhance" F15 fighter bombers for Saudi Arabia with fuel tanks and air-to-air missiles is a plain violation of a written pledge, made by Defense Secretary Harold Brown in May 1978, not to do just that.

"The word of the United States is very much in doubt in Israel, and for good reason," says one Israeli diplomat. In other words: the burden is not on Israel but on the United States to prove its trustworthiness.

How? Not, obviously, by withdrawing the offer of the controversial early-warning and command control AWACS airplanes to the Saudis. Begin knows that Reagan's commitment to the AWACS deal is irreversible. The crucial question, one on which the success of this week's meeting may well turn, is how, given these realities, he will behave.

The smart way, most Israeli and American authorities will tell you, would be for Begin to state his position and make his point; but to accept that if he lobbies heavyhandedly against the AWACS deal and Congress turns it down, he will have helped to humiliate Reagan in his first confrontation with Congress on foreign policy.

The merits of the AWACS sale may be arguable, but the transaction is a long way down the road. As a matter of tactics, accordingly, there is something to be said (and some informed Israelis are already saying it) for Begin to find a discreet way to go out and lose this one--for the Gipper, so to speak. That would leave him in a stronger position to turn the AWACS argument upside down--to ask, as an offset for the AWACS, for even more American weapons and financial relief.

Begin has been hinting at some sort of tighter defense alliance with the United States, without offering details. His aides speak of the need to redeploy at least two squadrons of F15s in southern Israel to counter the Saudi AWACS.

Somewhere in all this there is at least the possibility for something upbeat, especially if the security issues can be coupled with agreement on a common approach to the Camp David "autonomy" talks with Egypt, which are due to resume later this month. But it will take a delicate blend of U.S. toughness and Israeli restraint to produce a turn for the better in the relationship. There are more than enough ingredients readily at hand on both sides to produce a further turn for the worse.