PERSONALLY (and I might get flamed for this) but I wouldn't bother with upright rows. I don't like the position that they put your shoulders in. They aren't bad as a lightweight final burner, but since the idea to ensure proper form is to drive elbows as high as possible, you tend to increase the internal angle of rotation in the shoulder and weaken it. Slap on some heavy weight, and I believe you're looking for an AC joint injury.
If you've got back problems, I wouldn't recommend heavy OHP or Military Presses until you've gained enough strength in your supporting back muscles to perform them safely. Smith or BB Seated Presses to the front are both good options for a major - with side laterals or leaning side laterals good options for side delts. Rear delts can be performed on either a rear delt fly machine, bent over standing with DBs, bent over seated, or to an extent as Wide Grip (and wide elbow) BB Rows to the chest.
Good luck in strengthening that back - I know the trouble that you're going through if you've injured it in any way