Since it’s a “training” star for you, this probably doesn’t matter much. But I’d stay away from slower designs like the Turkina and Hel. They’ll have a hard time keeping up with the Jade Phoenix and Heirofalcon, especially in difficult terrain. I think 4/6/4 movement is the minimum for this star. Black Lanner, Flamberge, Night Gyr, Grand Summoner, and Summoner would be my Falcon omni preferences for this star. Nothing wrong with older Clan omnis like a Timber Wolf, Mad Dog, Stormcrow, or Nova. Or the newer Mad Cat IV or Vulture IV sold by the Foxes.
If you don’t care about keeping the star all omnis, there’s the Jade Hawk, Gyrfalcon, and the like. If you are watching BV, there are smaller Falcon omnis like the Cougar, Uller, and Ion Sparrow, but they’re fragile.
FWIW…