I.ii. The Wedding Banquet - Kline 90

The Kevin Kline version jumps right into the thick of things with a lustful kiss between Claudius and Gertrude (and they kiss again in the middle of the scene), catering to the baser animal qualities of the new king.

The staging is interesting here as the courtiers seem to orbit Claudius, almost moving about the room in a circle as he shakes hands with them.
Brian Murray's Claudius is gracious in his tactility, bridging the gulf between king and courtier, but though he is jovial, he's still a blowhard. There's one particular line delivery that I found strange. "Together with remembrance of ourselves" is played as clever word play that is immediately met with delighted applause from the crowd. There is no grief here.

Even Dana Ivey's Gertrude is unnaturally happy, apparently charmed by everything Claudius has to say, with a look of "oh he's so clever!" always on her face.
Either Claudius is a powerful charismatic or his courtiers are currying favor with their simpering flattery. Gertrude, however, seems completely taken in by his charms, heightening the emotional resonance of Hamlet's outrage and setting her up for a greater fall.

In contrast to Zeffirelli's private audience between Claudius and Laertes, their exchange is very public here as Claudius almost speaks more to the crowd than to Laertes (played by the soapy Michael Cumpsty).
Again we have a Claudius who is a social animal, living his life on a stage and relishing in it. Life as theater is the most potent theme of the play, and while we often look to Hamlet for its presentation, this Claudius is also an actor (as politicians often are). Hamlet Sr., the man of action (the warrior) is replaced by a man of acting who plays out grand conflict in public and with words. Consequently, though Cornelius and Voltimand are cut from the play, the message from Fortinbras isn't (tying off the segment at "so much for him"). Where Hamlet Sr. might have led men into the field of battle, Claudius gets applause for throwing a piece of paper away and undermining an opponent's threat level. It's a false military victory, all played in oratory.

But I digress. Laertes' suit is of course granted after a very stagy exchange (and I mean that to mean it was staged by Claudius, not as a directorial weakness). Claudius makes it plain that he is gracious and warm, and lets it be known that Polonius (veteran character actor Josef Sommer) is his right hand man.
If you have access to this version, check for the courtiers in the background during the "The head is not more native to the heart" speech for some almost parliamentary eyebrow acting. "Oh really!" they seem to imply. Where other stagings of the play have implied that this was common knowledge, here it isn't, and so the entire scene takes on that air of being a practiced spectacle for the Court.