USPS Expressmail is the best option.

It will guarantee next days delivery from most places on the continental U.S. It also provides detailed tracking information online. When you mail your package at the post office, the clerk will be able to tell you whether USPS will guarantee next day delivery.

FedEx next day service is great as well, but it is more expensive than the USPS express mail.

I would choose the USPS express mail. If your state is bordering Nebraska, you can even use FedEx ground. They are a lot cheaper but will also deliver your package the next day.