As I am applying for postdoc research position, I think the normal visa category that I am fit in would be J1 (Is that right?). Assuming that my visa would be J1, then what are your recommendations for me? Is it better to postpone my NIW application until I enter the US, or it is better to postpone my postdoc application?
Is up to you. If you enter the US on a J-1 visa, you should wait at least 60 days (and preferably 90) after entering the US with your J-1 visa before filing the I-140, in order to avoid possible visa fraud charges.