I just completed a J1 program in the US and departed a day before my grace period ended. Meanwhile, I would like to attend an annual conference of the organization of which I am a member in the US and also spend some time with family and friends. I would like to know how soon I can apply after J1 and what category of visa will be the best for my situation. B1 or B1/B2? I am a Nigerian studying in Germany.
You can apply for a visit visa immediately - and it doesn't matter whether you apply for B1 or B1/B2.
In practice, there's no reason not to go for B1/B2 - if you can convince the interviewing officer that you're a bona fide visitor, you'll get it. You may be issued a plain B1 visa depending on the circumstances, but like I said, no harm in applying for the combo visa.