A 7/8 Maine is called a purebred. If you breed your cow to a purebred bull, the offspring will be a 50% Maine(known as a Maintainer). The female offspring mated to a purebred bull will be a 3/4 Maine and eligible to show in the Maine class. You would need to have both offspring be female to get to Maine classification for heifer show, 4 year process. Any steer or heifer 1/4 Maine and up can show as a Maintainer in most shows.
As to sires, there are few purebred sires I would recommend at this time. I-80, Hard Drive, Mercedes Benz are maybe the most consistent.