You have to see them all. Between Gibson, Olivier, Brannagh and the BBC version, they're all different to the point of being nearly different stories. Gibson deals more with the Oedipal aspect. Brannagh's adaptation is nice, with some great casting choices, and his portrayal really comes across as pretty much batshit. Also, Derick Jacobi is excellent as Claudius. Olivier does a good job with projecting the ambiguity of Hamlet's mental state. The BBC adaption is quite good (as most of their Shakespeare works are), with Derick Jacobi as Hamlet and Captain Piccaard as Claudius. Along with Gibson's, it's the shortest of them.
If you're already well versed in the story, then you can start with any of them. Brannagh's is the only unabridged one, so it takes a little more understanding to get into. If you're not real familiar with the going's on, then I'd start with Mel Gibson's.
As for my favorite, I'd probably go with Brannagh's. The man's just got a good understanding of it all. Plus, some of the casting choices are pretty interesting. Heston as the player king was inspired.