@n80, it’s good to hear you are more intent on playing in a, as you put it, subtle style. While you might be able to pull off Keith Moon-style drumming in a few years (he played using single-stroke only, no doubles; you’ll learn what that means when you study with a teacher), the same cannot be said of Peart and Bonham. Remember, they had been playing for many years before they did any recording, and the number of years it would take for you to be able to play on their level might exceed that of your remaining lifetime!
Let me back up, and give you some basics. All musical styles require, first and foremost, a drummer be able to keep steady time. That seems obvious and not hard to do, but try playing along with a click track! Ringo Starr was excellent in that regard, better than many more technically-advanced drummers. Good singers are very aware of time (phrasing is one of their most important jobs), and are very critical of any drummer who doesn’t have rock-solid time.
If it’s old R & B and Blues you want to play, the first thing you need to learn is to play the shuffle/swing feel, the basic feel of Blues, Jazz, and Traditional Country. Neil Peart embarrassed himself in the drumming community when it became obvious during the Buddy Rich Tribute Show that he lacked the ability to swing.
The "press roll" is used a lot in R & B and Blues, and being unable to play it will be a pretty big limitation and liability. To play a press roll you need to be able to play more than single strokes, so I would say you should start by studying with a teacher who can help you with the rudiments. You’ll be glad you did!
I recommend you study the recordings of Roger Hawkins; he played on all the Jerry Wexler-produced Atlantic Records recordings done at Fame Studios in Muscle Shoals, Alabama: Aretha, Wilson Pickett, Solomon Burke, Percy Sledge, many others. He’s also on recordings with Etta James, Duane Allman, Paul Simon, Bob Seger, Joe Cocker, Linda Ronstadt, Leon Russell, hundreds more. He also worked with Traffic, at Steve Winwood’s request. Jim Keltner (another drummer you should listen intently to) said in an interview he wished he played more like Roger. Jerry Wexler proclaimed Hawkins "the best drummer in the world". His playing is pure brilliance!
In an interview, Steve Jordan (Keith Richard’s first-call drummer) said he considered The Band’s Levon Helm basically a Blues drummer. If you want to hear subtle playing at its finest, study the first and second Band albums. Drumming just doesn’t get any better than that! Those first two Band albums contain just about everything you need to know to be able to play drums really well.
Other drummers who will show you the way are Earl Palmer (impossible to imitate), Al Jackson Jr. (of Booker T & The MG’s), George Rains (Jimmie Vaughan’s drummer), Fred Below (Chuck Berry, Bo Diddley, Little Walter), and Sam Lay (Howlin’ Wolf, Muddy Waters, Paul Butterfield Blues Band).