I sent something similar last week. I put it into an old pill bottle, but anything that wont crush will work. Then I put the bottle into a padded mailer. It only cost $1.71 to send 1st class.
I ordered mine from ebay. Since you are new, would you like to trade. I'll send you 6 mailers, you keep 5 to use, you'll send the watch to me in the extra one. I'll even include the empty pill bottle so you can ship it carefully. In exchange you will ship the watch to me by first class mail.