I always start of by first drawing or making some ukulele scaled templates in the desired shape , then you can take the measurements of the parts you are intending to use and see if everything is able to fit on the ukulele .
once you know everything is going to work and fit you would have to look at some tools and how much you want to spend on wood and parts I prefer you get a some sort of saw that can cut out the shape of your ukulele ( such as a jig-saw , scroll saw or bandsaw ) you should also definitely need a router , any type should do …unless you are a real handyman and you feel like chiseling out all of the cavity’s by hand ….also some clamps and viles can come in handy as well )
now for wood , it’s really up to you …I chose to use very cheap pine because i am very new to this and I didn’t want to mess up a 50$ piece of wood ( but for my future builds I well definitely look at some hardwoods )
and for electronics …. this is also something that you should choose by your own personal preference but you should definitely have a pickup and output jack on your ukulele (and a volume control is nice to have too )
and then there is some stuff that’s really necessary for you ukulele like : bridge and tuners , you can get all of these parts in guitar building stores like http://www.stewmac.com/ and I got a special 4-strings electric ukulele bridge from ‘bezdez’s e-bay store’ for very cheap ( I’m not making commercial for all this , I’m just trying to give you some examples )and then you can pretty much start the project
(here is what I mean with making those templates)