Designing a printable button array

[BJG145]

Hi - I have a little knowledge of 3D modelling, but not how to design efficiently for 3D printing. I'd like to create something like this:

I'll be creating the button mechanism myself; they won't be bought-in switches, so they won't be anchored. I was thinking of arranging these within a grid on square shafts so they can't rotate, unless hexagonal ones would work better from a friction point of view.The main question is how to prepare this in a suitable/cheap/efficient way for an online 3D printing service. Would the buttons need to be printed separately, or could they be arranged in a 'sheet', perhaps within the holes for the shafts, ready to be cut out, or something...? Thanks for any thoughts!