Shoes with a navy suit... I start with what is OK for menswear, as the rules tend to be rigid and straightforward, at least traditionally so. American men should always wear black shoes with a navy suit, yet I think Italian style is to wear brown.
As for women, IMHO, you cannot go wrong with black shoes. But you can also wear grey (my fave), burgundy, yellow, fuchsia (if you are bold). Nude-for-you shoes are great in the warmer months, especially with a skirt or dress.
Navy is a neutral and can be paired with just about any color. If you are nervous, start with patterns that have a blue in them.