Keeping the toilet clean definitely became a greater chore after I got my J Pouch. Some of the suggestions made here are good ones. As far as stool on the seat, I don't think in most cases it poses a health issue but rather a cleanliness and hygiene issue. That being said it's still a good idea to use hand sanitizer afterwards and I always keep a bottle of Purell around for me and my guests, if I have any over to my condo. When I have overnight guests I clean all my toilets scrupulously and meticulously. I like Pine Sol for this task, as it leaves the toilets with a fresh odor of cleanliness.
Having a toilet with a very powerful flush also helps. The toilet in my master bathroom double flushes, and I kind of like it, even though I probably did something incorrectly in installing the toilet flush valve. A master plumber I am not, but sometimes a bumbling self-repair leads to an unexpectedly positive result.