How to narrow down choice of diode given max voltage and max current drawn
Would a Schottky diode be the most ideal solution to make this work?

That depends, if you want the cheapest solution then I think a Schotty diode might be the best choice. The disadvantage of the single diode solution is that some voltage (about 0.5 V) will be dropped across the diode. So the 5 V will become about 4.5 V. That might or might not be an issue for you.

If the 0.5 V voltage drop is an issue then you have other options like using a MOSFET based solution, see this blogspot.

I do not want to draw more than 500 mA of current, what part of the diode spec sheet would this apply to?

It depends on the diode's datasheet what this figure is called. For the SS12 (that's a very commonly used Schottky diode) it is called:

Maximum Average Forward Rectified Current  I(av)

For the SS12 this current is 1 A so more than enough for your needs.

+12V will be the largest voltage input for the project, so what range should I consider for the reverse voltage breakdown?

Anything above 12 V but add some margin so at least 15 V. You will be hard pressed to find a diode that cannot withstand more than 15 V. The SS12  can handle 20 V so also more than enough.

Is it considered good practice to add a capacitor to ground on the cathode side of the diode?  Or is that a specific design consideration (e.g. AC to DC rectified situation.)

You mean a bypass capacitor after the diode. Yes, that is good practice. You can almost never have too many bypass capacitors. As the diode does introduce some voltage drop depending on the current through it, the voltage after the diode will have a little more ripple on it. A bypass capacitor will help to eliminate part of that ripple.