There are many different kinds of chinrests. Most fit into two categories: chinrests that extend over the tailpiece and mount under the button, and chinrests that mount on the side.
And these come in many different shapes, sizes and materials, and have names such as Guarneri, Strad, Hill, Flesch, Dresden, Wittner, and Tekka.
With possibly one exception I will describe below, I do not "prefer" any one of these over the others because no two people are built exactly alike, and a chin rest that is comfortable for one student may not be a good fit for another. If your worn out chin rest was comfortable, I suggest replacing it with an identical model. Otherwise, you might want to head to a violin shop and try a few of them. Look for a violin shop that carries several different models and will allow you to try them. Your teacher should also be able to help evaluate fit.
Now, as promised, I will discuss the one chin rest that, for some players, I do recommend over the others. It is called the Gel Rest. The gel rest actually comes in several shapes, but its distinguishing feature is that it has a cushion made of a non-irritating hypoallergenic gel that fits over the wood in the rest. The company that makes the gel rest also supplies the gel toppers separately, and can make a double layered version for taller necks. The potential advantages of the gel rest are several. First, the cushioning of the gel reduces irritation to the skin from the chin rest. Second, it won't slip in hot conditions where sweating is an issue. Third, it helps the neck support the violin through friction between the neck and the gel. Finally, the cushion is more forgiving against the neck and often feels more comfortable to the player.
Below are some pictures of the gel and the various chin rest shapes:
