Your budget will largely determine which racquet you purchase, however a $300 racquet will not make a beginner play like Roger Federer. Selecting the right racquet for you will have an effect on your comfort levels while playing, and as a result, how well you are able to hit the ball and how quickly you tire out. Modern tennis racquets are light weight, and can differ in head size and shape between models. Ideally, you should test out several racquets to see how they feel in your hand before deciding on one for you.
Younger children are best off starting with a smaller scale racquet so that they are able to swing through the ball without hitting the ground. Just as important as the raquet are your strings - some string types and tensions are made for increased power, whilst others are aimed at increasing control. As you become a more proficient player, you will become more familiar with the type and tension of strings you prefer for your style of play.