You've got to use USPS or the shipping price will make you kill the deal...any other way gets into tariffs, ridiculous shipping prices, etc., Trust me, and the paperwork at the Post office is pretty easy and straight forward. Tom
Make sure it is well packed inside the case and outer carton. I have seen lots of guitars broken because someone dit not think to stop the guitar bouncing around it's hard case. Use old t-shirts or towels, bubble wrap. try moving the guitar inside the case if it can be moved so that the headstock touches the top of the case then when it's dropped it will hit there and there is a chance that the neck will break. Then inside the master carton make sure that it is protected front and back, top and bottom. Try to avoid using the small polystyrene fillers as everything sinks down through them. If you need to use them put twisted pieces of newspaper in as this helps keep them in place.
I can't advise which courier to use but always think of the one that offers the best cover, otherwise it is a nighmare when the guitar arrives broken. Take a few photo's while packing as well as the insurers always look for an excuse not to pay out.