Zero-padding won't help with the non-periodicity, will it? For that you may want to window instead.
Umh, it depends what you use the FFT for. You are right Stéfan when saying that Joseph should probably also use a window to get rid of the high frequencies that will come from the sharp steps at the beginning and end of his signal.
I had in mind the use of FFT to do convolutions ( https://en.wikipedia.org/wiki/Convolution_theorem ). If you do not zero-pad properly, then the end of the signal may "bleed" on the beginning, and vice versa.