You’re going to need at least a 6A supply for the leds, assuming a worst case of all 7 segments plus the decimal turned on.
As others have suggested, I would also look at multiple processors and break the display into 3, 12 character displays.
I don’t know what would determine common anode vs cathode in a new design, since you can make the rest of the circuit match the leds you choose. If you were driving several segments per micro pin, you would have to see which was higher, sourcing or sinking current, but I think you’ll end up with fets driving the leds.