I love this stuff...
For the more easily available stuff try The Reverend Horton Heat - the earlier albums are more hard and punkish and the later stuff is more purist, but you can't go wrong with the album "Liquor in the Front" which is kind of a mix of both.
Other bands to check out are Skitzo, The Griswalds, Nekromantix, Coffin Bones, Demented are Go!, The Mad Mongols, Frenzy and many more.
I used to go to the Klubfoot venue many years back (the Hammersmith Clarenden, now demolished and turned into a car park) and these Psychobilly shows were always 100x more violent than the thrash shows that were at the same place. Not saying that's a good thing, but that's just how it was...