Speed vs. Security
Speed: Fedex, UPS or USPS Express Mail. All are overnight and from Houston to Washington, DC, both Fedex & UPS offer delivery options as early as 8:00 AM.
Security: USPS Registered Mail. This almost certainly will not go overnight. Registered mail is sealed in front of you and is then logged into and out of each stop it makes along the way. For that reason, it is likely to take longer than regular First Class mail, but as noted it is as secure as it gets.