We were at Disney during a Monday on spring break and didn't get there until noon. Honestly the lines were not so bad, the worst was the line at WDW to get on the ferry coming home, after the fireworks show. The monorail was even worse, best seemed to be the resort boats.
Have fun and I recommend booking a character lunch or dinner in advance, somewhere to get out of the chill, take a rest and have a decent meal.