If you are looking to minimize the number of openings, note that one Black opening won't work because you can get very different games with the two most common white first moves, 1 e4 and 1 d4. The Caro-Kann 1e4 c6 and the Slav, 1 d4 c6, have very common ideas behind them, though they are not the most open games. Often, 1 d4 c6 2 e4 is played, transposing from the Slav to the Caro-Kann.
For White, if you play 1 e4, you have to be prepared for Black to play, at least, 1...e5 or 1...e6 or 1...c5 or 1...c6. That means four openings. But note that most games are out of the book by the 6th move, and studying a book like the one by Larry Evans and 6 other Grandmaster, How to Open a Chess Game will take you farther than rote memory of several openings. It's worth knowing an opening for each of those games that will lead you toward a playable middlegame - the main goal of the opening. For example, against 1 e4 e5, most people haven't memorized many lines of the Vienna Opening (2 Nc3) and the Bishop's Opening (2 Bc4), both of which delay playing Nf3 in hopes of getting a pawn to f4 early. Against 1 e4 e6 (French Defense) and 1 e4 c6 (Caro-Kann Defense), the Advance Variations - getting a pawn to e5 early results in a solid game. Against 1...c5, there are so many variations of the mainstream Sicilian that I often play 2 c3, the c3 (or Alapin) Sicilian so Black won't likely have an opening edge against me. The important thing is not to memorize move after move but to memorize the ideas behind the openings. You will also see almost every possibility against 1 e4: 1...Nf3, 1...g3, 1...b3, etc. That's where the Evans book comes in strongest.
These links look informative, so Im sure Ill get a lot better.
If numbers do not mean anything to you, what do you prefer playing as an opening and why?