Pick up one of these (heck, they're inexpensive, get two; one for the uke and one for your voice):
http://www.amazon.com/gp/aw/d/B003VP9VI8
Here's a review from a kinda well respected industry rag:
http://recordinghacks.com/reviews/tapeop/mca-sp1/
More tech if you want more:
http://recordinghacks.com/microphones/MCA/SP1
Later, pick up a Mackie 402-VLZ3 (used should be fine) the mic preamps are better than the Zoom. If you want American made, buy an older Mackie 1202 used. Take a line out from the Mackie, to the line in on the Zoom, and the Zoom becomes a basic digital recorder.
Now that you've done all that make sure you use the least destructive conversion method possible, otherwise it's all for nought.
Oh, one more thing. Get a free subscription to TapeOp magazine and a copy of the first TapeOp book; entertaining, informative, and invaluable reading for anyone interested in recording any kind of music on just about any recording medium (except, perhaps, wire).
Best of luck, hope this helps.