Circular polarisation is not caused by the spin of the satellite. The reason for circular polarisation is to make the orientation of the satellite irrelevant. If you were running a linearly polarised antenna and the orientation of the satellite was 90 degrees off, you could get end up with an effectively infinite loss whereas you can always pick up a circular polarised signal with a circular polarised antenna of the same direction.
If you have a clockwise polarisation but the satellite is sending an anticlockwise signal (both as viewed from the same end) you will need to change polarisation - which you can do with a crossed yagi setup (you effectively reverse 90 degree phase by feeding to one side or other of one yagi set)
You can't do that with a helical antenna - so you would need two if you want to pick up clockwise and anticlockwise signals.
It is not the spinning of the satellite that polarizes the signal. Rather, it is that a circularly polarized signal can be rotated without affecting the signal which makes circular polarization desirable.
This is not the case with linearly polarized signals: if the two are cross-polarized (one is vertical, the other is horizontal, for example), then the link will be extremely poor. As the satellite spins through aligned polarization and cross-polarization, you get deep spin fading.
There is no standard for which way satellites are polarized. Some are right-handed, some are left-handed. Sometimes the difference comes down to which was easier to build. Some satellites aren't circularly polarized at all.
If you build a right-hand antenna, this will work with circularly polarized satellites of the same sense, and also with linearly polarized signals with a 3dB loss. It won't work very well at all with an opposite-sense circular polarization on the other end. If you wanted to work left-hand circular polarization, you either need another antenna, or you need a different kind of antenna where the polarization can be switched. Helical antennas can't do this, but crossed yagis can.