WalMart, though I detest the place, does have a double-headed toilet brush, one side a full round head, the second a looped head similar to the old-fashioned veggie scrubber, which can be angled up to scrub around the rim. I wonder how I ever managed without this utensil.
Due to the nature of tenants, I use anything with chlorine in it. With really bad stains, I put a little LimeAway in the water and walk away for a few minutes.
I once had to clean a toilet which had been left full of *** and then dried out in a vacant house. Rubber gloves and a razor-blade scraper will pry this substance from around the edges and it will peel off in chunks, like peeling thick dried paint.