The best approach is preventative maintenance. I use
Lysol under-rim cleaner and as long I check on it periodically so that it never runs out, my bowl stays a nice antiseptic white forever. The only time I've EVER had to clean it was when I didn't pay attention to the state of the little puck and it ran out.
In the few cases where I've had to actually clean the toilet,
this works wonders.
Use it to clean up the stains then just pop the pad off into the garbage. But like I said, you should never need this as anything other than a backup.