The problem with cutting copper isn't cutting copper, It is when the beam isn't penetrating the material and just bouncing off the surface.
With a 1500 watt, I wouldn't go any thicker. And if you don't care about edge quality so much, use full power for pierce, full frequency full duty, and Oxygen at about 0.2 MPa or 2 Kg
If the edge is super important, use Oxygen for the pierce and then switch to Nitrogen, but cut super slow. 10 or 20 Ipm to start off with. Again, full power full duty.
Using Oxygen you maybe able to get it up to 30 ipm but start slow.
I would definitely baby sit the machine with my hand over any control that would close the shutter until I was confident that it wouldn't loose the cut. I'll have to get back to you on the coating.
Just like krugtech and laserninja told you, babysit the machine and don't walk away from cutting. Laserninja is right about using oxygen for cutting copper even if it's thin. I have cut up to 0.125" with oxygen on a 4.0 Kw Amada Gemini. Hairy at one point but I did it.
How bad is copper? Most internal/external optics are made of copper to reflect the laserbeam.