Quite a bit depends on more factors than you have stated.
It would be best if you and the research organization spoke to an attorney, to balance out the options.
Many of us use Skype for this type of meeting.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
H-1B is probably better. Depending on your circumstances, change of status to a J visa may subject you to the two-year foreign residence of INA 212(e).
Hake & Schmitt
Attorneys at Law
P.O. Box 540 (419 Main St.), New Windsor, Maryland 21776
Required Disclaimer: This information is generalized and should not be relied upon as legal advice; and this communication does not create an attorney-client relationship.