arduino/raspberry based current and voltage monitoring using Rogowski coil
I need the R-coils to measure current in buildings, so I need to be
  able to just clip them around the phases without removing the cables


So, why not use a CT with that clip-on clip-off facility. They are made and available: -






  I would like to have your opinions: using Rogowski coils, what kind of
  ADC/integrator (or integrating ADC) do I need (are there different
  types)?


I think that given a regular CT should be considered, this question is now irrelevant. There are plenty of ADCs but, if you really want to use a R-coil then you will need a linear integrating circuit like this: -



Choose R1 to be bigger than 330 kohm to ensure that it doesn't have an effect at 50 Hz - possibly 3.3 Mohm. Or make C1 something like 100 nF.