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If you want a CS Ph.D., demonstrate that you're a REALLY REALLY GOOD programmer; that can make up for lack of significant research experience. I've advised a few dozen students of various ranks, and I still rate programming ability as amongst the top prerequisite ... everything else can be learned more easily in a short time, imho:

http://pgbovine.net/prospective-students.htm

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They asked linear algebra and probability in the interview for machine learning in my school. Most rospective candidates got asked "what's an eigenvalue?" (among many other questions).

I guess what you should learn depends on the field. But they'll be looking for demonstrable interest and possibly outside learning.

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