I would go as big as possible as you will only wish you'd made it bigger when its finished.
I would have thought 3 ft depth would be ok as a minimum, enough to keep the fish safe during winter. Koi ponds can be 5ft or so.
Mine was going to be half the size but as I was the one digging it,I kept on moving the marker then I had an unfortunate landslide
, it ended up approx 18x19x4 1/2 ft at the deepest.Even my hubby says we should have gone even bigger.
My advice would be not to rush putting fish in once its finished,get every thing in place and up and running, feed the filter for a while to bring on the bacteria and check the water quality on a regular basis.
Look around for a reputable fish dealer and stick to the one source or you'll be asking for trouble.
Are you going to be using a liner?
And what type of carp do you want in there?
What filters have you looked at?
Will you be using UV? if the ponds in full sun you will prob need one.
Air pump??
the list is endless matey