I've ordered using a credit card from a whole other continent.. So that shouldn't be a problem
I prefer COD though, because a lot of the time the order will change from what you ordered, as invariably some things will be out of stock. Easiest just to pay the guy when he arrives.
Whether they will deliver when you're not home, you would need to arrange that with someone. Someone has to sign for the delivery and/or pay for it when it arrives.