Cost effective pickup
I found somewhere on the internet, not sure, but I think it was the cigar box guitar nation - that Piezo Transducers work. I thought is sounded a little cheesey, but I have now built four instruments using these and they actually work great in my humble opinion.
You can get the piezo transducer from Radio Shack part no. 273-0073 for 2.99, add in jacketed wire, mono 1/4 inch jack and solder and you have a little less than $10 invested. It is simply a flat brass disc, kind of like the little dude you find inside the greeting cards that play music, or inside el cheapo alarm clocks. The beauty is that you do not have to be spot on in order for this to sound good. I place mine just behind and the bridge bracing inside the uke. Wired to a jack, no pre-amp or controls and it worked out o.k. Maybe not as good as the pick-ups designed for that purpose, but a cool experiment to try on a junker if you have one.
Not trying to drop names or anything like that, but the flying fortress that dominicfoundthemoon has is set up this way, so he might be able to give you some feedback on the sound.