Sinks get pretty grungy. However, there are design features that make it get grungy even faster. On the flip side if you pay attention to a few key things during the design process, you could find yourself with an easy to clean, non-grungy sink/counter area.
In my experience, the key design features of an easy to clean bathroom are:
1) Counter level
The biggest issue I find with counters is that when they are installed they slope towards the back wall so that water pools by the grout.
Water pooling anywhere is basically an invitation to mildew to make a home. If your counter is installed properly then this shouldn't happen. Make sure you have a good contractor.
2) Counter surface
Obviously the surface of the sink and counter needs to fit with your overall design. All I can say is stay away from small tile and shiny surfaces. Bathroom counters with small tiles need constant cleaning and shiny surfaces look clean for about five minutes.
3) Sink edge
The best kind of sink is a sink with no edge. In other words a sink that flows directly from the counter material. This kind often has to be moulded for your particular bathroom so might not make sense cost-wise. The next best bet is a sink that is sunk below the counter surface.
4) Tap design and placement
The biggest mistake I see with tap design is a tap with lots of crevices, flat surfaces and a shiny finish. Gunk builds up in crevices and especially so where the crevices are flat. A tap with a shiny finish (similar to counters with a shiny finish) never stays clean-looking. Also, make sure there is enough room between the wall and the sink to clean behind it. I know it sounds obvious but I see this time and time again.
5) Water flow
The last issue and probably the easiest to fix is the tap flow. It is best to see if you can test drive your tap system before you buy it. A tap that is set really high might look pretty but it is bound to make a mess of things the moment the faucet is turned on. Water splashing everywhere is really only fun at the water park. If your heart is set on this design, see if you can adjust the flow of water so that the water pressure is turned down low. This might remedy the problem.
While all of these little details might feel picky trust me it will make a difference focusing on them before you renovate rather than fixating on them once you are finished.