Isopropyl alcohol, the sooner the better. Cat scatches aren't usually anything to worry about unless you have a weakened immuned system or similar. They can be ugly and if you have enough on your arms people might suspect you of cutting.
The bites that you really need to be concerned with are ones that involve deep puncture wounds. Usually you only get those by attempting to break up a cat fight or by really pissing a/your cat off. They can result in serious bacterial infections that will make you ill in the least or at worse, kill you, and I've gotten sick from it a couple times. The upside I believe is that if you do survive it will strengthen your immune system, you know "what doesn't kill you makes you stronger" in some cases, or so they say.
I don't think kittens should really be anything to be worried about though, and yeah you do get used to it and if anyone asks just tell them your cat did it.