The supporting table will be cherry. I'm contemplating buying one of the table base kits from someone like tablelegs.com, but not sure whether they strong and stiff enough for a granite top.

This is 2cm granite, with the edge laminated to make 4cm. For the cabinets, it is installed over 5/8" plywood, so that would be my default choice for the table.

How much deflection can be allowed? I've been using the "Sagulator" to calculate sag of the table apron. The plywood will provide a small amount of additional stiffness, as will the granite itself, but I'm not including those.

Any other good construction suggestions would be appreciated.

Gary

Basically zero.

Depending on ones definition of "basically," nobody would have any granite counter tops if that were true. Certainly true for my definition of zero. Basically zero is the value of your comment.

Even cabinets with sides all the way to the floor exhibit essentially zero deflection under load.

Stone is a brittle material, and cannot survive significant movement in its support.

You would likely require massive hardwood aprons (think both thick and tall) or metal under structure (think how a large fish tank is supported).

Why do you think the overhangs for granite counter tops are so small?

Metal rods cut into the underside or other metal supports are often required past about 12 inches (or less depending on the exact type of stone).

The longest counter dimension with 3 cm granite that is not supported is a DW, 24 inches wide.

You have to pick the correct metal shape.

You are incorrect about iron.
The flex of the metal can easily be removed as an issue with correct design and construction.

When chosen and used appropriately is will significantly stiffen wood.
You could cover the inside of the apron with about 1/8 in steel and have very little deflection (look up 'flitch beam').
It will take a number of screws and barely interference sized (about 0.001 or so) holes for the screw shanks
through the metal.

A piece of angle wrapping around the inside to the bottom edge would also add significant strength, as would just a flat strip on the bottom of the apron for its length.

A huge amount of flitch beam performance comes down to hole size in the metal matching screw shank diameter tightly, and enough screws and resulting bearing area to make the two material behave as a single unit and the wood does not crush under loading at the screws.

The screws limit buckling of the metal away form the wood so it stays flat in place with very little deflection for the composite assembly.

Angle are channel (open side down) are common since they have the vertical dimension required to get decent strength.

Just like strapping the bottom of joists with 1/8 in steel strap (plenty of flex there) stiffens the joists greatly The method relies on the fact that the bottom of the joist MUST get longer as the joists sag allowing even a floppy piece of 1/8 thick x 1.5 in wide strap 12 feet long on the bottom of the joist to stiffen it very significantly (the same as putting a huge wooden lip on the bottom of the joist)

Use number size drill bits that match the screw shank.

Remember the hole is ALWAYS a few thousandths over the bit size.

You might even need to try metric bits.

The most accurate holes are reamed after drilling them as close as possible (but still undersized).
Reamers come in 0.0005 inch steps (or even smaller).

For beefing up the aprons -- is it best to just glue the extra board to the inside of the existing apron, or should I also screw it?

I'm using the legs in the link. My table will be a foot shorter and and inch narrower than the one in the link. Cherry, stained almost black.

Make sure you use a glue that will not exhibit creep.

ALL the polyvinyl acetate glues have creep.

Elmer's, Titebond (in all it grades).

You need a resorcinol glue or hide glue (even the liquid hide glue).