How to find a capacitor for LDO that meets ESR requirements
Specification says, p.12


  "A minimum of 1 µF capacitance with an ESR of 1 Ω or less is 
  recommended to ensure the stability of the ADP151"


and


  "Any good quality ceramic capacitor can be used with the  ADP151, as
  long as it meets the minimum capacitance and maximum ESR requirements"


You will be very-very hard pressed to find a 1uF small ceramic cap with 1mOhm ESR, so you can safely ignore the contradictory statements from ADP151 specifications.

So the answer is: any ceramic cap will do the job, just as spec said.

ADDENDUM: There is no universal answer to a question at which frequency of the complex ESR(f) dependence one should look. The ESR itself doesn't define whether the LDO will be stable or not, the entire transfer function of feedback loop versus gain needs to be simulated to get proper component. As a simple answer one should look at the frequency where the LDO feedback amplifier starts to rotate signal phase substantially. The PSRR (Power Supply Rejection Ratio) chart might serve as a good indication where this area is, where the chart has some singularity. For ADP151 this area seems to be in 1-2 MHz area.