For mounting, you want the grill far enough from the cone to allow full excursion. The cone's linear excursion is specified as 5mm, but deep thwacks on a bass drum might exceed the linear excursion - I'd want more like 10mm space myself.
The more open area, the better. It's nearly impossible to get better than 65% with round holes, though woven metal or square holes can do a bit better. Most of the attenuation is in the treble, 5kHz and up.
In the bass and midrange, a high percent open area (POA) will be fairly transparent to sound. But it will still reflect a portion so there might be a resonance between cone and grill. You'll have to listen to it to know whether this is audible or annoying to you.
Are your cats likely to snag a claw and pull the screen off? Give some thought to a solid-enough mounting!