To make things a little simpler, here are the different sink options you have to consider:

Drop-In Sinks:

Drop-in sinks are the most common; as the name implies, they drop into a hole in the counter and sit flush with the countertop. These sinks are often cheap, easy to install, and could be a great all-around choice for your new sink.

Undermount Sinks:

Unlike a drop-in sink, under-mount sinks screw into the underside of your countertop. An under-mount sink installation can be substantially more expensive, yet they attract less mold and are easier to clean. 

Double Basin Sinks:

The defining characteristic of a double basin sink is a divider down the middle of the basin. The division allows you to use the sink for two things at once. The double basin sink has become one of the most popular on the market.

Integrated Sinks:

Integrated sinks are made of the same material so that the countertop and the basin are one seamless piece. However, there are limited materials to choose from, and they can be costly and hard to find for kitchens. 

Farmhouse Sinks:

A farmhouse sink is a large, single basin sink that sits flush with the front of the cabinets. Many people find farmhouse sinks desirable due to their sturdy builds, large basins, and beautiful aesthetics. Unfortunately, they tend to drip because there's zero counter in front of them to catch overspray.

Corner Sinks:

A corner sink is precisely that, a sink that fits into a corner on your countertop. Corner sinks usually consist of two basins with an integrated dish drying area. These sinks are a unique solution for kitchens with limited space and homeowners who desire maximum usable counter space. Like most other specialty sinks, corner sinks can be expensive and hard to come by.