Dill is actually related to carrots and like carrots it produces a rather large central tap root. When planting dill keep this in mind, the depth of the container should be suitable for hosting a large root, at least a foot deep preferably a tad more. Dill is also an annual, grown for a single season so you shant have to worry about it accumulating excess roots from one season to the next.
Once all danger of frost is gone, you may want to keep your potted dill plants outdoors, it is advisable to wait a tad longer as dill is not a cool weather plant and does best in warm, but not hot temperatures.
Any variety of Dill can be grown in a pot, but the more compact varieties are best, especially for novices. Try Fernleaf a dwarf dill variety or Dukat another compact variety which works well in containers. See: Dill Varieties.