A minor theory lesson on Got A Ukulele with something that you may find useful - the Circle Of Fifths.
Below you will see a Circle of fifths chart that you can print off and keep in your songbook. It's called a Circle Of Fifths, because going clockwise around the circle from the 12 o clock position are all twelve musical pitches, going up by a fifth each time. Laying the pitches out like this allows you to work out lots of cool things.
Firstly, you can use the Circle as is to immediately tell you what chords go well together in any specific Key. Take the key of G Major for example - locate the G on the outer wheel. The Circle tells you that any chord that touches that G box will work "well" in a song in the key of G, i.e. C, D and Em. The next closest but not touching chords (The Am and Bm) may work also, and the further you move from that G box, the harder it will be for the chords to work in that song. It's not a firm rule, but a good general rule of thumb. That relationship works as moving clockwise from any Key you move to the Dominant (the V) of the previous key. Moving counterclockwise you move to the Fourth (IV) of the previous key. You would be amazed at just how much of popular music rotates around those note relations (i.e. I, IV, V) - and they do that because they sound naturally pleasing to the ears.
You can also use the Circle as a transposing tool - that is to say a guide for changing the chords in a song up or down in keys. You may have a song sheet that you really like, but you just can't make it work for your voice. Print off two copies of the Circle, but make one copy smaller. Cut out both circles and separate the inner from the outer ring. Putting the smaller of the outer ring copies inside the larger, you can now line up the change in key you want and automatically work out what all the other chords change to. For example, say you have a song in the key of G, but want to play it in the key of C, lay out the larger ring with the G at the top. Put the smaller ring in so the C chord is lined up with the G. Now you can use that smaller inner ring to read off what new chord you would need to play for any of the original chords (Still following me....?)