Is it acceptable to have a unique wedding invitation even if you are planning a traditional wedding? Absolutely. While some people like to coordinate their invitations with the style of their wedding, it is not strictly necessary. If you have a fun or different idea for your wedding invitations, then, by all means, choose the invitation that you want. If you plan on celebrating with a formal ceremony, make sure to mention that on the invitation, such as "black tie requested". On the other hand, if the wedding invitation is off_beat people may assume that your wedding will be a more casual affair unless you specifically state otherwise. Putting the information on the wedding invitation prevents any confusion.
In olden times the bride's parents paid for the wedding so the invitations would be issued by them, but now it could be the couple themselves or both sets of parents who are paying, so you'll need to agree between yourselves who is to issue the invitations.