The second thing I tell them is to stop working on their resume and find a band or bands to play with. There seems to be a huge information gap out there when it comes to the practical realities of studio playing. Aspiring drummers are aware of some of the demands of studio playing but unaware of the experience necessary to perform well.
live experience is important because each night and situation is different. Playing live also develops your natural time, which is a huge help when you start working with a click. There is no better place to improve your knowledge of styles and musicianship than the bandstand. These skills lead to the maturity necessary for studio work.
Reading different kinds of music is important. The best way to achieve this is to play in reading situation. Theatre gigs help a lot because show music has meter and tempo changes much like the stuff you will see in the recording studio.
Confidence born of experience is one of the most important factors in studio playing. Composers, whether they be Paul McCartney or Danny Elfman, never think about what is playable when they are writing. They just write it.
Awesome technical skills are not necessarily the ticket either. I learned this as I chatted with a jingle producer one evening at a club. The conversation turned to a very famous drummer who was the hottest player in town. He dropped a bombshell when he said that he couldn't get four bars of real time out of the guy and that everything he played was stiff.
"Make it feel good" is the only absolute I know of in studio playing. The feel is what makes notes into music and is a drummers most important tool in a business dominated by technology.
the groove continues...