Many people seeking to improve their chess games have the same questions: What opening system should I be studying? Which attack or defence is the best one for an inexperienced player? While there are many good opening systems that pack surprises like traps and gambits which will give you an advantage over less prepared players the best advice I can give as a fellow beginner and student is DON'T!
Don't worry about learning partiuclar opening systems just yet. This is a common rookie mistake many of us have fallen into! Before you try and memorize long lists of moves and theoretical lines, without really understanding *why* such moves are positionally accurate, try and understand the underlying pawn structures that can arise from any system.
To put it simply, pawn moves are permenant; Unlike the pieces they cannot move backward. By following the foundational opening principles of development, you will begin to see patterns arise that are common between the various opening systems and have similar strengths, weaknesses, and objectives. Believe it or not these qualities will be largely determined by the structure of your pawns!
There is a fantastic video (about a half hour, so make a cup of coffee!) by Daniel Rensch that was created as an introduction not only to structural play, but to an entire series of videos that take you from a basic understanding of what pawns are all the way up to the fine details of advanced structure. http://www.chess.com/video/player/pawn-structure-101-introcomplex
It is far more important that you understand why you are making the moves than it is to memorize what moves to make in every situation. That way, when you are playing someone who makes a move you are not familiar with (whether it is a line you haven't studied or simply someone who doesn't know what the 'right' response to your moves is) you can still make an informed decision about what is happening in the game, what your opponent is or should be doing, and what you are or should be doing based on the current setup of the battlefield.
All that being said, I do understand that sometimes you just want to study some lines or learn some traps in order to have a quick way to surprise less advanced players, or make you somewhat competitve against more prepared players. For this I would recommend investigating what tend to be the most common positions reached when both parties follow the opening principles:
The Four Knights Game
The Italian Game
The Ruy Lopez (aka Spanish Game)
The French Defence
The Sicilian Defence (this is a heavy subject, but nonetheless a very common one. The most deeply researched opening, one can get lost for years studying the many lines and variations that evolve from 1.e4 c5. Best saved for later, but can lead to exciting games too!)
The Modern Defence (aka The Robatsch Defence)
The Queens Gambit (check out mainlines for both accepted, and declined)
The Kings Gambit (also check out both main lines)
You can also use the chess.com Game Explorer to see what the most common moves are at high levels to each postition, and follow them through right to the source games. If you don't have a Premium Membership, you might want to consider grabbing one to access all of the great tools here!