Karl,
You never want to design your program to have to use the run continuously button. It is more for debugging than anything else. Using a while loop with your own stop button is the preferred method of doing things.
The System, 3-D, and Classic Booleans all basically work the same. The appearance is different. The System buttons look like your OS buttons that you see on all your other programs. The 3-D were introduced in LV6 and remain standard across different OS's and are not affected by System color changes or System theme changes. The classics behave similarly to the 3-D, but they are the older controls that existed prior to LV6 and have been kept for legacy's sake.
There are arguments for using system controls vs. 3-D controls (I don't think most people use the classic controls much anymore). So, you really have to make a personal decision as to which you prefer to use. NI pushes the system controls, but you'll notice there is a large number of controls which are not available in the system pallette. I have made versions that look like system controls, but they do not automatically update for theme or system color changes.