What are the most important documents?

Social Security Card. Once you arrive to US you must apply for Social Security Number at the nearest Social Security Administration office. Social Security Number is issued to you just once and it is a very important document in the US. If that number was not issued to you, you might not even get a job and will not be able to get your tax refund. Contact Social Security Administration or your J-1 visa sponsor while in the US if you have not receive Social Security Card.
US Visa.
Last pay slip. Your employer will pay your salary by issuing the check. Each check will have a pay slip attached to it. On the pay slip you can see what salary was paid to you, and what tax deductions were made. Keep all your pay slips secured, especially the last one, which is used for your tax refund.
W-2 form. This is the final document from your employer, where you will find all the information about your income and tax deducted while working at the company. This document will be mailed to you after the end of financial year - the 31st of December. Work and Travle participants should receive W-2 forms by the February 15th. You should receive separate W-2 form from ech employer.
DS-2019 form (J-1 visa participants)
Details about your employer. Company's name, address, payroll department telephone number.