I think the primary interrogator should be not an Elected Representative but rather a professional attorney because the selfish interests of committee members to get face time on television wrecks the whole narrative by destroying its coherence and prevents it from proceeding logically from a beginning to a conclusion. Moreover, the interruption every 5 min. for Democrats to question with the equal time makes it difficult for the lay observer on C-SPAN to make sense of the preceding.
Above all, it would be a blessing from heaven if the Democrats are foolish enough to actually follow through on their threat not participate.
I would assume that Boehner will behave decently, that is, he will keep his hands off the subpoena process, granting the committee broad range of subpoena power and complete independence and selecting staff and procedure of conducting hearings, as far as House rules allow. How much independence Gowdy is able to negotiate for himself with Boehner is critical and we will probably not know what Gowdy had to give up until long after this inquiry enters the history books
Finally, it is not actually the public hearings where the real productive work will be done but in the examination of documents, diligent demands for those documents, tough interrogations, judicious use of limited or general immunity, and deft relations with the press who will be at best passively aggressive and perhaps even openly hostile.
