Design direction for invitations is typically informed by the nature of the client, the event (or other) that is the subject of the invitation, the demographic of the target invitees, any branding considerations and print considerations such as paper weight, paper-texture, and so forth.
Shape, orientation and folding considerations should always be considered and discussed early with the client, and the cost implications of any potential design options should be identified at an early stage.
The client's budget is always the bottom line and is the primary design factor for physical design considerations, such as the inclusion of rice-paper, ties, multi-page options, creative folding, etc.