What is the best variety of rice or preparation of rice to use in soup?
I've found that the most consistent way is to use short grain rice that is prepared much like it is in Indian cuisine. I was taught to rinse it repeatedly until the standing rinse water runs clear. That seems to remove most of the starch that causes that sticky breakdown. 

Also, I've found that making rice soups in a slow cooker can be made less sticky by adding the rinsed rice after the other ingredients have settled in and become well heated. I've only dealt with this a couple times, so I definitely recommend experimenting if you prepare your soup in a slow cooker. Good luck!