Since this is an articulated model, you'll want to make sure you don't have any printing issues such as stringing or overextrusion that might bind moving parts together! You'll also want your first layer to be nice and neat, since that's the bit you'll see when the lid is closed!
For a nice colour effect, try swapping the filament after the first two or three layers, or even changing the filament multiple times! The holes in the pattern taper inwards to a point, so multiple colour changes should give an "outline" effect to the pattern. Don't forget to print the ring at the same time, if you're using the threaded version! :)