You can never go wrong with Courier. Naturally, you should follow any specific guidelines that a publisher provides.
Do not use Courier New if you can find a darker Courier. I know that a lot of style sheets will say to use "Courier New," but I doubt that anybody means this to be taken literally. Courier New just happens to be the version of Courier that everybody has on Windows computers.
There are also these versions, which look essentially the same but are darker than the anemic Courier New:
Courier10 BT
Courier MM Screenwriter
Courier Std
Courier Final Draft
Dark Courier
And if you convert a document containing Courier New to a PDF, it usually gets converted to Courier (Type 1), which is very slightly darker than Courier New.