I disagree about priority mail, unless you can send it certified with return receipt.
The best way is to overnight it or send it by FexEx's cheapest way, which will be able to track your envelope and track who signed for it. This option will tend to be expensive, though. FedEx has a new ground shipping option that is worth checking out.
The way I plan on sending it is to send it regular mail, but get it certified with return receipt. Basically, it goes through regular mail, but you attach a post office post card which the recipient signs and dates. The post card is then removed from the package/envelope and mailed back to you. If you can do this Priority Mail, which is supposed to take 2-3 days, all the better. The cost of this will be around 3-5 dollars.
Certified mail costs $2.30 plus postage (60center - $1 for most apps). THis means they have to sign for it, and you can contact the post office to make sure it was delivered, and see who signed.
A return receipt is postcard is $1.75, and you can do this by itself or in connection with certified mail. This postcard is sent by the post office when they deliver your mail.
SIgnature confirmation, another option, is similar to this return receipt, except the the addressee actually SIGNS the postcard before it is mailed back to you, instead of the post office just mailing it back.
Priority mail is fast, but you do not get delivery confirmation unless you add it on.
You can also do a delivery confirmation that you check online for 55 cents (45 center for priority mail) instead of teh postcard.
pretty much the cheapest Fedex option is still going to be considerably more expensive than USPS certified mail. A 8x11-sized envelope will run around $10 for 2 day delivery but this includes all the tracking features. USPS priority mail doesn't have tracking unless you pay extra for it and even then, it's only updated once a day with minimal information. Fedex is constantly updated with detailed info. With certified mail, you get a receipt of confirmation sent to you via mail and I don't believe there is any online tracking. Personally, I trust fedex more for really important pieces of mail, we use it in the lab where I work regularly and have never had any lost or misdirected packages. The customer service is also impeccable. Sorry if this sounded like a fedex ad.