If the seat doesn't appear clean (as in free of visible anything), I look for another toilet. I use the paper liners if provided. PLEASE: clean up after yourself, whatever your method! This includes making sure whatever you deposited in that toilet is GONE.
But I have a question about the tampons -- I thought one of the whole points of tampons is that they are flushable? (Not the wrappers or applicators, but the tampon itself.) Am I crazy?
Anyway, if you start thinking about the germs lurking in a public bathroom, you would never go in there. The poster who said the faucet and door handles are your biggest source of problems was exactly right.
I wash my hands, dry them, then use another fresh paper towel to turn off the faucet and open the door. Ugh. I hate bathrooms that only provide the hote air blower, no towels. What about the splash water all over the counters, sinks, etc. Nasty. Bacteria love dampness.