Scoring points is the name of the game and you can't do it without rocks in the house. That's probably going to require some draw shots. These shots require some knowledge about what the ice is doing and a bit of finesse from the thrower. Some good sweepers are also helpful! It might seem strange to think about such a delicate shot as aggressive play. The skip is being aggressive by getting into scoring position and putting the opposing team on the defensive. Guard shots are also considered offensive play, even though they serve to "defend" a rock in the house.
Good curlers will employ a combination of these strategies depending on a number of factors including who has hammer, the score, which end you are playing, and even the skill level of your teammates. Probably the most important factor in your strategy is your opponent. You don't know what they are thinking, so you have to be ready to adjust. Watch your opponents shots and find their weaknesses. Then make them throw the type of shot they don't like to take.