I don't know much on the issue personally, but in Person and number in pronouns: a feature-geometric analysis (Harley & Ritter, 2002), they make the following claims:
...a language never has a dual without also having a plural (captured by the fact that both Group and Minimal must be active to encode dual). Similarly, no language has a paucal without also having a dual.
This seems straightforward enough, and under this claim, languages with a paucal must have at least 4 numbers (singular, dual, paucal, plural). However, they make some concessions in the footnotes:
Corbett (2000:39) makes a distinction between determinate and indeterminate numbers. Singular, dual and trial denoting exactly one, two or three individuals, respectively, are determinate numbers; paucal and plural are indeterminate ones. We have not explicitly encoded this distinction in the geometry, with the advantage that it enables us to deal straightforwardly with languages that allegedly have a paucal without a dual, such as Bayso (Cushitic) or Walapai (Yuman), cf. Corbett (2000:22) and references cited therein. In these languages, the paucal denotes between two and six individuals, rather than the usual case of three to six. We propose that a dual is a simply a determinate minimal group, and that the paucal in Bayso or Walapai is an indeterminate one, represented by the same Minimal Group geometry as the dual.
So it seems that the previous paucal-dual claim has counterexamples. Still, there must be a singular-plural distinction before a paucal can appear, and it is quite likely there will be a dual as well.
They make another interesting restriction on number related to the paucal:
Note that we predict that no language has both a trial and a paucal number; they are in complementary distribution, representing determinate and indeterminate interpretations of the same geometric configuration.
And of course, no typological study is comprehensive. I'd be happy to hear more on the issue myself. ;)