I believe that all realcent members who ship pennies in quantity use flat rate boxes. Either of the regular sizes are fine. Weight limit is 70 lbs.
You could definately buy insurance-but will you be able to collect on it? Since the pennies are "cash" and generally you can't insure cash, I question the wisdom of paying for insurance on the package and personally don't insure shipments. If you can't afford to loose $50-$100 face value in pennies I would not recommend shipping your pennies through the mail.
“The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.” – George Bernard Shaw. Why Copper Bullion ~~~ Interview with Silver Bullion Producer Market Harmony Passive Income blog