This page attempts to visualize various resampling kernels in a way that will help to you choose which one is right for you. There is no "best" kernel -- they all have their uses and the right one for will depend greatly on both the source and personal preference.
Start off with a common choice, like Mitchell-Netravali or Lanczos3. If it doesn't look acceptible, compare them with other kernels on the graphs to find one that has better properties in the area you wish to improve.
The X axis represents the distance between the optimal sample location and the actual sample location. A dead-on hit would be at 0.0, while a hit one pixel away would be 1.0, and so on. Note that kernels can take multiple samples.
The Y axis represents the weight applied to the sample at that distance. Note that most kernels have negative weights at some distances.
Note: The graphs below require a web browser with HTML5 Canvas and Javascript support to display. Any modern browser like Firefox 3.5, Chrome, and IE9 should work. If you don't see graphs, upgrade your browser!
Here are some of my own observations:
Mouseover the kernel names to highlight the corresponding line on the graph.