I played in a a few rockabilly/psychobilly bands, and Ive used a variety of kits. Even though you are talking about a music style from the 50's, the 60's kits sound great to for this music. The wood combinations and the rounded bearing edges are pretty much the same from the 50's to 60's. And the 60's drumsets are ussually a lot easier to find. I used a 60's Supraphonic excusively for live gigs, and a 60's Slingerland Artist maple for recordings.
Unfourtunatley I noticed that most of my audience, band members, and even recording engineers never cared or could tell the difference between one of my vintage kits or a Pearl Export house it. Of course I cared and it made a huge differnce to me, but it was always a sad fact (of a vintage drummer's) life.
As far as heads I've never used calf, but would love to. I would think calfskin would really give you a beautiful rockabilly sound, but I have heard that calf can tear easliy and is much harder to work with due to humidity and its effects on heads. Some of those bars can get pretty steamy filled with bodies on got summer nights. Ive used Ambassadors and always thought they sounded great.
Now I play in a jazz trio, sub for other jazz combos, and work almost exclusively in jazz, and it is just such a different world. Most people, especially my musicians can tell the difference between kits, heads, and the respect for a good drum kit, with good sounds is like night and day compared to the rockabilly world. Plus no one bumps into or spills beer on my vintage kits! (Once "backstage" I found someone leaning on my 22" Rogers bass drum, and I almost nearly killed them!)
Good luck trying to find the perfect rockabilly drum set/sounds, and remember that some of us do take notice and appreiciate it!