score:2
You need to present:
Both passports (the new one open at the main ID page, the expired one open at the visa page)
Either the blue customs form you get and fill out on the plane (if flying to a non-APC airport) OR the receipt from the APC kiosk (if you fly into an airport where you can use it - in this case you don't need to fill out the form)
(on request) Invitation letter from the company with contact Details
(on request) Return flight confirmation.
If they ask, just tell the truth: you'll attend a conference for one day and then travel around as a tourist. No problems with that.