As for dark make-up around the eyes, I would suggest a varied route on which you wanted to take/ how much you were willing to spend.
It looks to me like the reference picture you're using isn't actually make-up but rather a shadow created by the hat/hair itself. However, when i do make-up for female costumes its best to properly layer yourself before applying the actual color. This is to make sure it doesn't rub off or flake off, then you end up with fall-out all over the rest of your face.
Most of my products I use are either MAC, or name brand, remember that the more expensive make-up you buy the better quality it produces.
There are also creams and other regiments which make a color more prominent.
These are called primers. It's a cream that goes overtop of the eye mostly, but help to prevent creasing and flaking when wearing ti for long periods of time.
As for applying the dark areas yourself: Perhaps try a black or a dark grey eyeshadow, you wont find other colors unless you're using a liquid makeup. If you choose to go this route remember that a little liquid goes a LONG way. and to prevent smearing and smudging of liquid make-ups (especially when most cons are during the heated seasons!) you will need to go over the make-up with a finishing powder, and then perhaps a seal. The powder will prevent smudging or smearing, while the seal will prevent rubbing off onto your wig/costume.
Hope this help! Anything else just inbox me.