Newbie needs help, just got an "old" uke, loose neck...

I have been looking for a cheap ukulele for a while and just found one at a local thrift store. I haven't had a chance to really get using it as it is missing a few strings, but I have noticed that the glue holding the neck on is breaking down and the neck has a bit of give to it. I am not totally sure, but I believe that I have a 1960(ish) Harmony. It looks exactly like the one posted here:
http://antebelluminstruments.blogspot.com/2009/09/c1960-harmony-baritone-ukulele.html
though I am not sure if the size is a tenor or a baritone. The rest of the uke is in great shape-- no cracks or anything, though the fret board is getting a bit dried out.

I guess I am wondering what to do about this neck-- is it something that is worth having repaired or is the Harmony not worth fixing? Do I need to worry about getting the neck fixed before getting strings on it? Thoughts would be very appriciated!

Probably worth fixing, if there is a guitar shop near you take it by and see what their luthier thinks, it may be an easy fix and not be to expensive. I'm sure there are some more experienced floks here that will be able to give you better info than I can on how to fix it yourself.