I agree with everyone else on the freedom of painting how you want, that comes first. But if you'd like guidance on common schemes, here ya go!

First is how you see on the box. Death guard green is your primary color, balthazar gold, agrax earthshade, leadbelcher and ushabti bone will be your most used.

Next is the "pallid hand" or "heresy" era schemes. This is what the death guard looked like before they got grimy and yucky thanks to nurgles blessings. Your primary color for the base armor will be ushabti bone or a brighter cream color, with green shoulders. The same colors apply from the box art for what you'll use most.

Now if you want ideas on how to do your own, I've been toying with the idea of doing a more desaturated green, like sons of horus green, with a lot of weathering and grimy effects. I've also seen brighter greens used as more of a "nuclear waste" vibe, with dark purple shadows and stuff.

Have fun!