What are your criteria for evaluating potential PhD students?
I take a two-phase approach (US, computer science Ph.D program). First, I defer the initial judgement to our admissions committee (unless I have identified a specific prospective student I am trying to recruit).
I then look through the admitted students for potential candidates, and focus on research record, statement, and LORs. I'm looking for evidence of (potential for) critical thought and reflection, not just buzzwords.
Once I've identified a candidate or two, I arrange for an interview.  A few days in advance of the interview, I send them a recent paper either by my group or a group working on related topics to read.  I try to pick one with a low barrier to entry for understanding (feasible in my research area), and then in the interview ask them for (1) a summary of the paper's goals and (2) a question or two it raises for them. At this stage, I am not looking for perfect answers or good research questions, but the first steps of the ability to read something and think about it. I also ask some other things in the interview, such as why they want to do a Ph.D (even if this is in their statement - I want to hear it, and ask questions).
I'm still pretty junior, so I haven't had a lot of time to refine this yet. But so far it seems to be ok, and it lets me see whether we can start to talk about research, and can also surface fundamental incompatibilities in goals or research philosophy (although some of those come up in the LOR too).