IMHO, it has as much--if not more--to do with the builder of the uke as with the woods. Much depends upon the following:
a) solid wood vs. laminate
b) mass-produced, production model, or single luither custom job
c) setup (nut, saddle, string width, height, and action, et cetera)
Most seem to agree that the soundboard (top) has the greatest effect on sound. Not just what type of wood, but how it is braced as well.
That said, general opinion holds that a solid spruce top will generally bring out the brightness of the soundbox. A cedar or redwood top, by contrast, tends to be warmer and bring out more midrange and lower frequencies.
For back and sides, mahogany and koa are traditional woods for ukulele luithery. I've heard great ukes made with both. Depending upon the luither, they can both make great soundboards too. Maple tends to be a brighter sounding wood. Then there's walnut, sycamore, rosewood, myrtle, acacia, mango, and a host of others I've read good things about. All different, but all capable (in the right hands) of making a great uke. Most can be "googled." Might be a good idea to do a few searches on woods on FMM and you'll find much. Try "tone woods," "spruce," "koa," and "mahogany" for starters.
As always,
YMMV.
My best advice would be, if you're thinking about a custom, 'tis best to talk with the luither and get her or his perspective on the sound qualities of various woods.