To keep it classic, we are using Cuban bread. It's a hearty white bread that can sometimes be difficult to find in stores. If you can't seem to find it, substitute with French or Italian bread.
You can use deli ham such as black forest, smoked ham, and even honey ham. You want to use thicker sliced ham as opposed to the thin sandwich cut variety.
You can still make a delicious Cubano without a panini press. Simply cook the sandwich on a griddle or in a skillet. Use something like a cast iron pan or heavy bottom skillet to press the sandwich down while it's cooking.
These are very hearty sandwiches, so feel free to reduce the amount of the ingredients to fit your tastes.