There is no best sex position to conceive a baby.
While the goal is to have the sperm as close to the cervix as possible, in general, the sexual position you choose will not have any bearing chances of conception. There are no studies to support that any one position increase the likelihood of pregnancy.
As for your post-coital routine, healthy sperm will begin swimming immediately after ejaculation so there is no need to lay with your feet in the air after intercourse to help them out.
When a patient comes in for treatment, we do advise they lay still for 5 minutes after their embryo transfer and treat their bodies as if they are pregnant until it is time to take their first pregnancy 2 weeks later. That means no alcohol, a healthy diet and only moderate exercise.
Find out more about seeking treatment at Shady Grove Fertility by calling 1-877-971-7755 or click here.