We've seen several launches, and each one can be different, depending on time of day, weather conditions, etc.
Remember, you're still 60 miles away. It's very difficult to see the actual shuttle itself as it's barely a dot in the sky. You will clearly see the bright flame. In the day the smoke trail it leaves behind is really something.
Are you by any chance planning a Sea World day during your trip? I don't know if they still do it, but they use to televise the launch on their big screen at Shamu stadium. This helps the waiting time as you have something to see, and can watch the countdown. Then when the launch actually takes place, you can look to the right of the big screen, and see the real thing off in the distance.
If you watch from WDW, just be sure to find a place with open ground between you and the East. Even at that it will be a little time after liftoff before you'll be able to see it, as it has to get pretty high before it's visible 60 miles away.
Warning, if it's a low overcast day, you may not see anything as the shuttle may disappear into the clouds before it gets high enough to be seen from the WDW area.