A few years ago I explored 1950's rockabilly mainly from listening to Cramps, Stray Cats, Dave Edmunds, Rev Horton Heat etc from 1980s and wanting to go back to original guys who started it all......as said before many of biggest names played for Sun Records, although there are plenty even more extreme lesser known artists on smaller labels.
Perhaps best to get one of the large Rhino collections, for 1960s psychedellic music the Rhino Nuggets collection is great, for 1950's rockabilly I have:
Loud Fast and Out of Control (unfortunately not sold new anymore)
The Rhino "
rocking bones" collection mentioned above is still being sold and is the one to get new.
Keep in mind the sound quality of many of these is not great and some will sound more like revved up country songs vs rockabilly, but still good fun.