I select FedEx (either Economy or Express) because they've been super reliable for dozens of shipments from MyUS. I've gotten to a first name basis with our FedEx delivery guy and he always calls me to check if we want the package left when we are not home. He's even popped back at the end of the day to drop them off on occasion. The budget economy option is slower and doesn't state who they use to ship. I prefer certainty, particularly on such a high value item.
Got no idea what that term refers to but we've never had any issues with receiving packages so I wouldn't worry about it. Might be something to do with customs but they collect GST so it won't get held up. Also their postcode has 0 US sales tax applied so you won't get charged that on top of GST.
The MyUS membership has a US$60 annual fee but it is waived for two years if you use either the Amex offer or Visa offer. Just google MyUS Amex offer or Visa offer and you will find the links.