Prior to smoking, I don't use anything to clean/prep my mouth, other than maybe a swig of water. While smoking, I am usually drinking coffee or water, but I drink coffee or water all day when I'm not smoking too, but as I have whole bowls at a time, once I sit down, I like to stay sat down until I finish, I don't want to get up to make anything, and I usually smoke with my afternoon coffee, though I'd have the afternoon coffee even if I wasn't smoking. That's my relax time.
I will though see if I need to use the bathroom before I sit down, can't risk having to stop to go inside and coming back to my pipe having gone out, you lose man points if you can't keep it lit the whole way through.
After smoking however, I have some water then brush my teeth with regular old toothpaste (and I mean PASTE, not that gel stuff—nothing wrong with the gel "paste" as far as I know, just don't like the taste/texture). And that's all I do.
I have non-alcohol mouthwash (Crest prohealth something or other, white bottle with blue label) and a waterpik that I also use as regular oral care, but not specifically after smoking.
As to nose and throat, I don't do anything for them. If my nose or throat is bothering me, I don't smoke. Smoking hasn't aggravated either for me.