Openings are generally categorized as Open (double K pawn), Semi-Open (1.e4 followed by a Black move other than 1..., e5, such as Sicilian (1..., c5) or Caro-Kann (1..., c6) or French Defenses (1...., e6) or Closed (Double Q pawn). I wouldn't necessarily say that these bring about a draw more often. If you are adept at them, you can strangle you opponent slowly rather than dispatching him quickly. The result is the same.
The double "e" pawn openings are called open since the pieces come into contact with each other sooner and tactics abound. Conversely, in the closed openings early positional maneuvering takes precedence and tactics are delayed. The semi-open games lead to unbalanced positions with both sides having chances. These will be fighting games as a result. As the other respondent has indicated, it's normally suggested that you start out with open games to gain tactical experience. When you say being careful of counterattack, I assume that that's what you're referring to, and it's always a good idea to examine those for both sides. Tactics are not absent from closed games, but the opportunities for same usually take longer to arise. You'll still need to be adept in them regardless of the type of opening though.
I'd suggest that you look at an opening manual to get a better idea of the different types of opening. I don't advocate memorizing long lines of play though. Just try to get a basic understanding of each.