If you are not using a vanity, your sink will probably be a free-standing or a wall-mounted style. These sinks use very little space, making them ideal for a small bathroom. They are also highly preferred in bathrooms fitted for accessibility. Whether they rest on a pedestal or attach to the wall, the plumbing will be visible (considered a downside by some). They also offer no storage space. In addition to actually requiring less space, these models make your bathroom appear larger.
If you are including a vanity, you might choose the smoothness and sleek continuity of a solid surface vanity top and sink. This is one continuous piece that includes the sink. This style is also possible with stone (granite, marble), cultured stone and concrete. Stone and concrete will require sealing and resealing. These sinks tend to be shallow as compared to some other styles.
Drop-in sinks have a rim that overlaps the edge of the countertop. These are inexpensive and easy to install, making them a great choice for the do-it-yourselfer. Look for a style that has some depth to limit splashing on the surrounding area of the countertop.
Under-mounted sinks attach to the underside of the countertop. These are very popular because they create a smooth surface that takes full advantage of every inch of surface space. This style of installation, however, limits your countertop choices to a material that is completely waterproof (no standard laminate or wood and no natural stone or concrete unless it is carefully sealed).
Countertop installation has become very popular in recent years, although this trend is beginning to wane. This type of installation uses specialty styles of bowls which sit atop a counter or piece of furniture. These styles tend to be costly and installation can also be expensive.