Welcome to the site vmaxftw! I believe that the biggest tire you can squeeze into the stock swingarm is a 180. You most likely will have to do the washer swap to achieve this though. I run a shinko 170; it fit with no problems and no washer swap.
If your looking to go bigger with wheel/ tires your going to have to have the swing arm modified. If your staying with the 15" wheel your going to be limited to staying with a bias ply tire. Most wanting to go the route of a wider rear wheel/ tire get a 18" aftermarket rear wheel so they can convert to radials where there are many better tire selections. The front tire can be fitted with a radial as is, but do not mix bias and radials, as you probably already know.