I love these fixer uppers. They really challenge you. Here is a quick sketch of a suggestion as to what to do with the breezeway, along with inspiration pics. I'll be posting four pics for the overall exterior, four pics for plantings and four pics for the interior of the breezeway. I hope this will give you some ideas!
1) Ok, don't get nervous. The breezeway will now become your new main entrance. Close up the existing entrance and add three additional windows.
2) My guess is that you now enter straight into the living room. By using the breezeway, it will create a very welcoming front entrance and a good size foyer with hanging for coats and shoes from the garage and the front entrance. Keep the existing breezeway windows and door and brick facade. Put two large out-of-scale pots under the windows on either side of the new front door for flowers or evergreens under the windows.
3) As mentioned above, an arbor over an extended front patio will highligh the front entrance. Enter the front patio from the driveway. The patio should extend past the front of the garage about 4'-0". Of course, all of this should be drawn up and approved according to your local permits.
4) Add a small window over the garage doors and add a weathervane over the garage. A cobblestone or stamped cobblestone concrete driveway would be nice, too.
5) What color do you want to paint the house? Do you have a preference? This will determine the finishes for the garage doors, the new entrance door and the arbor.

This house is definitely a diamond in the rough. Can't wait to see what you do. Good luck!