For this situation I would recommend Audacity. This is how you can do it in Garage Band. To splice, simply double click on the track you want to splice, go to the slider that popped up and go to the bottom section of the track. Here you can select, select what you want to delete and ether 1, double click to make it into a separate clip or 2, press delete. To quantize it, go under Audio Region, click on the drop down under "Quantize Note Timing" and select the timing, this will quantize the whole track. If you click in the top section of a track, you can drag waveforms to the correct position. I will put pictures if you are still confused.
