eleganza -- I think mixing black and brown could often work, but personally I wouldn't were brown shoes with a black dress. Black would work, or some other fun color like red.
Jillian -- I think some peep toe or round toe pumps would be great. Or maybe some high heel sandals. I wouldn't go for anything pointy or wedges. If you post some you own, or some your considering buying to go with the dress, I can let you know which I think would be best, but it does seem pretty easy to match to since it's a simple dress.