Sink size is of the utmost importance, especially if you simply wish to replace an existing sink without modifying the cabinetry. Remember that the hole in the countertop can be made bigger but not smaller, i.e. you can buy a larger sink for your existing countertop but not a smaller one.
Three types of sink exist: single-, double- and triple-bowl models. Some come with an integrated drain board. If you decide on a double- or triple-bowl configuration, make sure that the dividing wall between the bowls is lower than the outside rims, to prevent water from spilling over onto the countertop or the floor.