I would suggest that you give a listen to Cream, especially their live work. Jack Bruce and Ginger Baker did a lot to redefine the "rhythm section" away from just supportive to voices in their own right. As for "falling down the stairs", I think Ginger pretty much nailed that on his recorded drum solo "Toad" from the "Wheels of Fire" album. Nothing against Neal Pert or Carl Palmer, they are both excellent drummers.
My personal favorite has always been Mitch Mitchell, from the Jimi Hendrix Experience. He incorporated Elvin Jones' style of "circular drumming" to good effect in that band. Sometimes Mitch's playing and fills were a "wash" of sound as a backdrop to Jimi's playing, and it was Noel Redding who nailed down the time and meter on bass. Noel had his moments too, and was a pretty good bassist for a guy who was actually a guitar player!
I'm a bassist who started out on drums, and picked up guitar later on. I learned bass by listening to Cream, Hendrix, and the Beatles. The one other major influence on my bass playing was Phil Keaggy, who taught me a lot about moving bass lines, getting around on the neck, and hand position, as well as a melodic approach to the instrument. He's even more unsung as a bassist than he is as a guitarist, and he's one of the world's best guitarists. If you don't know who he is, Google him and check out some of his work!
The older I get the more I appreciate, am floored by, the Beatles. Who even comes close?