The very first time you run AppleWin it may seem to have locked up. Don't Panic. The faster a processor you have the longer it will sit there. What it is doing is calculating how to go from X Gigahertz down to 1.54 Megahertz.
You can have it run at Apple ][ speed, at your full machine speed or something in between.
In the case of Ultima III you will most definitely want it to run at Apple ][ speed. If you are on a ship, running at full CPU speed, the wind will change so fast that you can not even move. Even if you just hold the arrow key down constantly.