The sound of the drums for that type of thing really comes more from the miking, treatment, heads, room, tuning and of course, the player! Coated Ambassadors or calf heads, fairly muffled, medium tuning (R&B in the 60s was primarily played by jazz cats so the tuning on records pre-1970 was a little higher). And not too many players then hit as hard as today's players. Bass drum wasn't as busy then so it didn't need to be as dead. Even the sizes play a larger role. i.e. a 3-4 piece jazz or standard rock kit with an 18"- 22" kick and 12"-13 and 14"-16 toms is more suitable than the giant super monster kits of later years. Those factors are exponentially more important than the brand itself.
That said, I've tried them all and for what you're going after, any brand will work. If you're letting the toms ring more and are seeking specific tones and are particular about tuning - Rogers will give you a versatile sound that is kind of both modern and vintage. Ludwig or Slingerland are more alike. Not my cup of tea but perfect for what you're going for. Gretsch is a whole 'nother animal and Camco has a bit of all of those brands. Those two are the brands I prefer. But since the sound you want is fairly dead/muffled, any of those or even a foreign brand or a cheap Japanese/stencil kit will do the job for literally a fraction of the price. Good luck!