Geocoin shipping can be a daunting task for most folks.  I'm going to drop some tidbits of information here I've learned over a few years of selling them.  Remember though, your mileage may vary :)

Shipping sources -- I've always used the United States Postal Service, herein as USPS.  They are by far the cheapest shipping source you will come across for items as small and light as geocoins.  They offer a wide range of options that can fit even the smallest seller

Shipping options -- USPS offers several shipping options.  First Class, Priority Mail, and Parcel Post are a few.  I ship the majority of my packages via First Class, since they typically fall below the 13 ounce cutoff for Priority or Parcel Post.  With the First Class option, you can add items like Delivery Confirmation (currently $.75) to see when the item left the Post Office and when it was delivered, Insurance to cover loss or damage, etc.

Shipping costs -- I never ever ship anything other than First Class unless weight becomes an issue (13 ounces).  Why?  It's a huge waste of money.  Priority Mail simply guarantees that you will pay more.  If you read the USPS website, the Priority policy is 2-3 days or more.  Well, why pay double or triple the cost for "or more"?  Shipping studies have shown that Priority arrives in the same time as First Class in more than 90% of the cases.  It's simply outrageous.  Also, if you have to go heavy, try Parcel Post.  It's quoted as 6-7 days, but some shipments have gotten there in 2.

Packaging styles -- When shipping a geocoin, always use a bubble mailer.  Don't get fooled trying to scam the USPS out of a few pennies and pack it in an envelope.  Experienced packagers can properly tape and cardboard items together to maintain the 1/4" requirement for a first class letter, but it's hard to pull off and not consistent.  Geocoins have sharp edges, and will even cut through the best of bubblers on occasion. 

1/4" thick to 3/4" thick are considered large envelopes or "flats" and are a great way to save money if you don't need extra services from the USPS.  They are typically ~ $.30 lower than a parcel, and first class flats arrive in the same time.

3/4" thick and above are considered "packages" or "parcels".  This shipping will cost the most, but it will allow you to add insurance or delivery confirmation to your package.  Unless it's 3/4" thick a proper USPS clerk will reject those services even if you ask.  In order to make your geocoin package 3/4" thick, wrap the item in bubble wrap, packaging foam, old mailers, etc until the whole thing swells.  It's also a good way to keep the item from shifting during transit and tearing the mailer.

Mailers -- There are two main types of bubble mailers.  Paper mailers and Tyvec mailers.  Paper mailers are generally yellow paper, lined with bubble wrap.  These are pretty sturdy, and inexpensive.  They are great for small light shipments that don't shift a lot during transit, so the coins don't tear out.  Tyvec mailers are a bit more expensive, but rarely if ever tear during transit.  They are made of a polymer material and hold up to heavy loose shipments very well.

Hopefully this helps a bit when trying to get those geocoins to arrive in one piece.