The best color to get good coppers, or any chestnut agouti for good rufus, is chestnut agoutis with good rufus. Unless the other colors have a pedigree of animals with strong rufus behind them, you will not get a good deep color (too much black surface color).
Red will give you a clean color, but it will turn your undercoat from slate to cream, not what you want with Coppers. It is recommended every few generations, but it will mean you will have to cull for a while to get what you want. This is a great read.
http://www.asrba.org/varieties/Copper_Satins.pdf
I do not, use any Reds in my Chestnut agoutis, though I suspect the otter buck I recently got carries Red, and I have a really nice clean chestnut kit now that makes me suspicious of him. Mainly because tort is not acceptable in my main breed, and I need to look at my SOP out in the barn, but I don't think it is in Satins either. I'll get back to you on that one.
I have rainbow peds, and let me tell you first hand, my chestnuts agoutis have suffered greatly. Although my otters have excellent rufus because of it.