Hello from JustAnswer.
The risk in women with Factor V Leiden is primarily associated with the contraceptives that contain estrogen, so the combined oral contraceptives. The evidence for risk associated with progesterone is mixed, and they clearly are much safer than the combined contraceptives, but the progesterone contraceptive that appears to consistently carry the least risk is also the method that involves the lowest systemic levels of progesterone. So, the safest and most effective method for contraception would be the use of the progesterone IUD, called Mirena. The oral progesterones, such as the mini-pill and the morning after pill, may carry a low level of risk, but are much safer than the combined contraceptives. The morning after pill is a good option when unanticipated sexual activity occurs and occasional use would not be associated with any significant risk of clotting, but in a woman that is regularly sexually active, frequent use of the morning after pill is not as effective as either the IUD or mini-pill. Injectable progesterone, such as Depo-Provera appears to carry slightly greater risk than the oral progesterone-only pills.
Of course, non-hormonal methods of contraception, such as a diaphragm, would also be an option.
So, once you become sexually active, the Mirena would be the most effective and safest long-term contraceptive for you, assuming that there are no other contraindications to the Mirena. But if you engage in unanticipated sexual activity, then it would be fine to use the morning after pill on an occasional basis.
If I can provide any clarification, please let me know.