Since a wedding is a traditional event, no matter how untraditional your wedding may be, I would suggest you send your wedding invitations via the post office, but choose an invitation that is eco-friendly.
There are many stationery companies that create invites that are 100% green. A quick Goggle search will bring up hundreds of results. Some companies will offer invites printed on paper sourced from cotton (Crane & Co), while others will use recycled paper. They use inks made from vegetable dyes as well as embellishments, like ribbons and bands, made from recycled materials.
An e-vite may seem like both an eco and budget-friendly option, and while I think that evites are fine for save-the-date cards and the rehearsal dinner invitation, a wedding invitation should arrive in a real mailbox not a virtual one.