We can open games in many ways (any of the pawns or knights) and then go ahead with different strategies. The queen being the most important piece, I would like to get it out in the field without compromising the security of the king and using a minimum number of moves. Which types of opening and/or moves would facilitate this? Also provide any pros and cons to your strategy.
I don't think that getting your queen out early should be your goal in the opening. Fighting for the center, developing your pieces, and king safety should be your priority. That said, e-pawn openings are your best bet to open lines for your queen as soon as possible. Look into the Ruy Lopez:
[FEN ""] 1. e4 e5 2. Nf3 Nc6 3. Bb5 ...