I don’t think there can be, or needs to be, a “best” drummer of all time. There are so many incredibly talented players that to determine a best would be selling short a lot of great players. IMHO, musicians shouldn’t be in competition with each other.
Having said that, some of my favorite drummers are:
Steve Gadd: The epitome of a studio drummer. Incredibly creative, with a groove that just won’t quit. Listen to “50 Ways to Leave Your Lover” by Paul Simon to hear an example of his artistry. His discography is huge and you have probably heard him more times than you realize. Steely Dan’s “Aja” is another examply of his brilliance.
Vinnie Calaiuta: Drummer for Frank Zappa and many many others. Vinnie is probably one of the most technically proficient drummers that has ever lived. A good example of his playing would be “Keep It Greasy” on Zappa’s “Joe’s Garage”.
John Bonham: This man invented hard rock drumming as far as I’m concerned. Sure he was one of the hardest bashers, but he could also play with finesse and always had a rock solid groove.
Steve Smith: Don’t let his work with the pop band “Journey” fool you. The man can play some jazz and has chops that are to die for. I recommend any of his work with his band “Vital Information”
Carter Beuford (sp?): The groove behind “The Dave Matthew’s Band”. I think he is one of the most innovative drummers around. The fact that he is completely ambidexterous makes for some very interesting drumming.
So many things. A rock solid sense of time is a must. Being versitile. Ability to not overplay and rather, play for the music.
I don’t think that you have to see a drummer live to determine how well he plays, although some drummers excel more at live playing and others in the studio. I think an ability to improvise can really show the depth of a musician, not just drummers. It’s one thing to play something that you have had a lot of time to work out the details. It’s quite another to just be able to play with anyone in any style and be overflowing with ideas. To me, the best drummers display this ability.
Good luck with your drumming quest. If you choose to study, find a good teacher and play in as many different situations as you can. Drums are awesome:)