With that kind of power capability I'd run romex, probably 14 gauge assuming AC, just to be on the safe side. You have a nominal 1800 watt power source there. CAT cable, 23 gauge, would act like a big resistor and easily overheat under dead short conditions. Even if you ran two CAT cables and used all the conductors of each for each side of the output of your transformer I wouldn't be comfortable with it, if it were me.
Looking at the thread area, I assume that you meant to say 30
VA not 30
A. A very large difference but you'd still need to use multiple conductors to be safe. Nominal wire size for a
doorbell is 18 gauge. Why not use some 18/2 thermostat wire and be done with it. You could pull a CAT cable along with it to future proof for a PoE doorbell in the future.