What backwards, paranoid, anal retentive planet do all you people come from?
There are no rules for which stall to take; just pick the first clean one with paper.
Need to pick up a tampon on the way? Go for it. Anyone who's uncomfortable with the existence of tampons is in the wrong restroom.
Speaking of which, if you're at someone else's house, be mindful of what you flush down their toilet.
Were you talking to someone who entered the restroom with you? Keep talking even when you're both sitting on your porcelain thrones, especially if it's a friend or sibling or someone you know well. The exception to this guideline occurs if the person you were talking to is someone like your new boss. You might want to wrap up the conversation before you enter a stall or let them decide whether or not to keep the conversation going and then you can pick it up as soon as you're both face to face, just for the sake of professionalism. If they're done before you or you don't want to talk at that particular moment, tell them you'll catch up with them or to just give you a minute or whatever. Don't you women have girlfriends who you go to the restroom with all the time when you're out at a restaurant or club?
For Pete's sake (and anyone else who may shake your hand at some point in time), Wash Your Hands! I don't care how often you shower or how clean you think you are; there are germs all over that stall and germs don't sit still. Did you touch the door handle? Did someone else who maybe isn't as fastidious? Did you touch the toilet or did your hands get within an inch or so of touching it? Did you touch the area near the little disposal for feminine hygiene products? That's the dirtiest area in the entire restroom.
And one more thing. The lines at women's restrooms are longer because it simply takes longer on average for a woman to use a restroom. There's no big secret to this. If men didn't have urinals and washed their hands, they'd take just as long.