Can I apply for B1/B2 or F2 and what are the required documents for both?

You indeed may be eligible for such nonimmigrant visas for the purpose of staying in the U.S. temporarily. The choice between the two may depend upon your goals, such as intended length of visit. The Office of the Foreign Student Advisor at the university your wife attends may be a good source of information about applying in the F2 nonimmigrant visa category, and should be able to explain the process as well as discuss advantages of that option, without the cost of engaging an immigration attorney.