It depends on what you want most from the transaction. Since you did not mention your whereabouts, I'm going to assume you're American (because Americans often don't think to mention where they are). And that the recipient is in the USA as well.

If speed is the top priority, send USPS "Priority Mail Express." It will arrive in 2 days to all locations in the USA (usually 24 hours to most locations). There is tracking at every stop. You can check a box on the Express Mail form that requires the recipient to sign for the envelope, but that is waived by default. Make sure they will be around when the Postal worker comes by to deliver their mail or they won't get it if they have to sign for it. It costs about $20.

If you want tracking but want it relatively cheap and fast, send it by Priority Mail. It's about $6, has tracking, and will usually arrive in 2-4 or 5 days.

If you absolutely cannot afford for the envelope to get lost in the mail or the contents stolen no matter how long it takes, use USPS Registered Mail. It's insured up to $25,000 and has chain of custody and is signed for by every person it is handed off to. It is somewhat expensive (~$13) and takes up to 2 weeks for delivery.

USPS mail has a much lower chance of being opened by unauthorized people and having its contents stolen than do parcels sent by couriers (UPS, FedEx, etc.).