Really depends on what kind of watch you really want. Those choices are very different.
Anyone who has seen my WAYW posts knows I'm partial to JLC in general and to my Reverso in particular. However, I wear it primarily as a dress watch (I know it is the original sports watch, blah blah blah, but in this age of Pams and such it is a dress watch). I have skinny wrists, so I have the classic duo. Here are some shots from the archive . . . .
Reverse (I hardly ever wear it on this side):
The Royal Oak is a monster sport watch. IMO it looks good on your wrist at the club, driving your Aston Martin on the weekends, sailing your yacht, or engaging in heavy demolition work. If you accidentally blew your arm off, I'm pretty sure the watch would survive. I have never liked the look of that AP, but it is a quality watch.
The rolex is a nice compromise between the two. Although it is clearly a sport watch, its relatively clean look makes it a good choice with a suit as well (again IMO). I wouldn't wear a metal band with a suit personally, but I think that it has become so commonplace I am now in the minority.
My choices, in order, are JLC, Rolex, then AP. In terms of quality, I'd go JLC, AP, then Rolex. In terms of what will hold its value the best, I'd go Rolex, JLC, then AP.