Hi Gonzalo-
The Vcm is provided as an output on AD9625, but is not required to be tied to your balun. It is used internally and can simply be referenced to GND with a capacitor.
Yes, the choice of balun or amplifier for your system is critical to the performance. The selection will be dependent upon the bandwidth needed, the input power required, and the tolerance to distortion from the phase and amplitude mis-match introduced by the front-end components. The baluns that I listed are the first choice for the best performance.
Thanks,
Ian Beavers