personally i think "best" here is contingent on what you're looking for from a shakespeare film or a "shakespearean experience." that is, i tend to think of shax films in terms of what they're trying to do with shakespeare, how interesting that is, and whether or not they succeed. for sake of the answer i'm gonna limit us to direct productions rather than adaptations like Scotland, Pa, the very best Macbeth riff that is built entirely out of a McDonald's pun.
Branagh is a great example to start with because his 90s run of shakespeare films were indeed very well regarded, but notably, their entire deal was to make certain lushly produced and historically set shakespeare films that were pointedly about finding the very notion of shakespeare awe-inspiring. his 1996 Hamlet for example was the first cinematic filming of what we call "the complete text" (ie, what you'll get if you buy a Hamlet paperback off the rack today). this totals a four hour runtime, which is absurdly long--but our "complete text" is composed of sections from distinct and different printings, that probably historically arose in different drafts and repertory iterations. in other words, the "complete text" of Hamlet was probably never conceived of by or performed in shakespeare's time as such, but it gets assembled by editors as they focus in on it as his "greatest play" and try to include all the best bits of the different printings. so Branagh's deal here is premised on the idea that for the first time a shakespeare movie is going to Give You Everything, As It Was Meant to Be Seen, but that's downstream of a whole bunch of shakespearean mythologizing. that's not to say it's bad--i think it's a very solid film, actually--but it's also aimed squarely at a certain sort of anglophone cultural industry crank and/or the classroom.
let's contrast that with Franco Zeffirelli's 1990 Hamlet, which has a reduced text (most stagings do, too) and despite being historically set relies on two very different draws than Branagh: the first is casting action star Mel Gibson in a role that's famously about delaying action, and the second is tapping into Zeffirelli's history via his well regarded 1968 Romero and Juliet, which is quite romantic and erotic in that 60s European way. so Zeffirelli's Hamlet ends up focusing more on romantic and erotic intrigue, in particular dialing way, way up oedipal readings of the play and Hamlet's fixation on his mother (played by Glenn Close, who at this point is associated strongly with Fatal Attraction and thus the whole erotic thriller subgenre). is this interesting? certainly. but is the film good? no, i think it's actually pretty embarrassing.
we can dogleg out here and see a second-order contrast with Luhrmann's 1996 Romeo + Juliet which dispenses with the softness and mannerism of Zeffirelli's version to instead lean fully into the adrenaline-and-hormone-soaked Teen Love. on the one hand it tosses the stuffy historical setting, a seeming gesture of iconoclasm, but also ultimately works to suggest shakespeare's ongoing relevance by claiming it has found a hotrod beneath the hood of the stodgy old packard. that's a pretty smart maneuver, it smartly edits the playtext in line with that thesis, and the movie whips ass.
downstream of all this: Michael Almereyda's 2000 Hamlet is trying to do the Luhrmann thing, sort of, but is less successful. it can't nail ennui in the way that Luhrmann nails the terror of adolescent love, and while Luhrmann's stylization dates his film but also makes it endearing, Almereyda's Y2K aesthetic is simply less lively. as far as how it engages with the play, it reduces the text and chops and screws the order of scenes so much that if you know the basic causality of the established play you will notice it truly does not actually make much sense. BUT the movie sort of seems to know this--Ethan Hawke's Hamlet is a film student and his "play within a play" turns out to be an impressionistic video montage. so what, on the one hand, is kind of a bad Hamlet adaptation in a straightforward sense is actually thinking pretty smartly about what it's doing in a conceptual sense, even if the final product is sorta muddy and limp.
if pressed to choose an ultimate favorite shakespeare movie, i'd say mine is Julie Taymor's 1999 Titus for a couple of reasons. one, rather than the classics i've been describing Taymor is taking what was historically considered one of shakespeare's oogiest plays and treating it seriously (and in fact, we might credit her film with basically rescuing Titus Andronicus, which is now regularly staged in a way it historically was not). two, she performs this feat by refusing the implicit historical/presentist dichotomy of all the films above, being thoroughly postmodern by strategically having different parts/aspects of the play evoke different historical eras in ways that are thematically resonant. third, she relies a bit on intertextual casting with Anthony Hopkins, but doesn't let the Hannibal Lecter association dominate his performance, and indeed, sort of lets him affectionately parody himself by tapping into Lecter's inherent camp value while also just being a generally great actor. notice, of course, that michael lutz's favorite shakespeare movie happens to be the one that makes the most michael lutz moves, and might not translate for people who aren't him...
i still think you should watch it. but if you're looking for an entry point on the big name plays, Branagh is solid and broad appeal.
except for his 2000s movies, where he starts doing the lesser comedies with conceptual settings on a tight budget. his heart is in the right place but those are bad. there's a reason they only let him play hercule poirot these days
