Sperm: Fertility Center of California estimates that if artificial insemination will be the treatment method for conception, there should be at least 3-6 ICI or IUI vials PER pregnancy attempt. This means that if you would like to have 3 children someday, you should try to have at least 18 quality ICI or IUI vials stored for future use. Please note that a vial is not the same as the number of days that a collection was performed. Depending on sperm concentration, some males may be able to freeze 1-2 quality vials per collection, whereas other males may be able to freeze more per collection day. It is different for each male. If IVF is the method of treatment for conception, generally fewer vials are needed as less sperm is needed for IVF-ICSI treatment, but it is also based on what the embryologists would prefer, so please check with your IVF facility for their recommendation.
Eggs/Embryos: It is hard to comment on the number of eggs or embryos needed for conceiving a child because it is dependent on the quality of the eggs or embryos. This would be a good thing to discuss with the embryologists at the IVF facility.