It very much depends on context. If you want to stick strictly to key of G, then C is suggested. If you simply have two lines a third apart then either could work and your ear should tell you which is better in the circumstances. You do need to consider what is happening before and after and how the two lines work horizontally as well as vertically.

If you have other things going on then you may find you get a nasty clash if there is a D in another part and it will be much worse with a C#. If you have other instruments playing and there is a D chord, I would be inclined to play a D over the A rather than a C or C# unless the clash gives an effect you want.

I quite often add harmony lines by first transposing up or down a third or sixth, then going through and making changes to suit the key of the piece. While playing or singing in thirds generally sounds OK, varying the interval generally makes for more a more interesting/pleasing harmony overall.