I've used Expedia quite a few times and always been very happy with them. Prices are good and service is good too.
In my experience, when checking into the flight, I have not been asked for my e-ticket, only the passports. The check in desk computers have a list of names booked on the flight and use your passport. Not sure if this is always the way (but it has been when booking on EasyJet etc, only passports, no tickets had to be shown).
Another tip - if you plan to 'check-in' online before the flight (as we intend to do when we fly to NY next year) you will need booking refs and e-ticket numbers which aren't automatically given when you book. Expedia will email these to you if you request it.
Have fun in the US!! It's fab!!!