See my blog on baby thank you notes
Besides purchasing invitations, it must be decided who will attend the baby shower. There is no limit to who may attend, especially nowadays. One consideration is to send out invitations to people who know the mother well enough to buy something appropriate for the new baby. Also know that invitations sent to people who do not know the mother are likely to be considered a bit rude. On the other hand, not only those very close to the mother may be sent invitations.