Answered by Bryan, Hiring Expert at IBM Corporation, on Wednesday, June 25, 2014
This is a good question and can absolutely be different for each individual based on their specific J-1 visa rules. Your home country might have a rule that you need to come back for a certain amount of time before you are able to work again within the US. You should not have issues with an Intern or Co-op opportunity as that is more easily managed with a J-1 visa while you are in school.
There is quite a bit of detailed info you can find on the US Department of State website about J-1 visas using the following URL:
Not all countries that take part in the J-1 Visa have a rule that would make you have to move back home for any specific amount of time. In that case, a company would more easily be able to take you through the H-1B process after you graduate. Just know that there are only 65,000 H-1B visas approved each year in the US (not including the 20,000 for students in the US with Advanced Degrees), so you may still run into possible issues with receiving that limited work visa.
My recommendation is that you reach out to the group that processed your J-1 visa to learn about any rules that would require you to move back to your home country for any specific period of time. That will help you create a game plan for what steps to take for a future opportunity in the US.