What's the best career?

I'm not sure about the Beautician, but the rest allow piercings.

Chef will always have plenty of jobs, people need to eat after all. Pay can be anywhere from 20,000 a year to 80,000 depending on the place you work, your rank in the kitchen, or if you're working for a rather wealthy individual. Piercings are often allowed, but some times you need to take them out for safety reasons. Tattoos are generally not a problem.

Body Piercer is not a glamorous life. Every piercer i've talked to about it said that you get paid little, if anything when you're apprenticing to become one. You will have very little free time while apprenticing, and then when you actually become one you rely on sales and tips mostly. You often have to pay fees to studios in exchange for working out of them. You won't make a lot, but it's enough to get by on. Obviously any body modifications are welcomed with open arms.

Hairdresser's make probably 30,000 to 40,000 but i'm somewhat unsure of that. Once again I suppose it depends who you're doing it for. You might make even more if you work for celebrities or in a more famous salon or something of that sort. They rarely care about piercings.

Unfortunately I can offer you nothing on beautician. Take everything I say with a grain of salt, though I have looked into chef, and body piercer, i've not looked into hairdresser. My memory of their salaries are minimal, and I can't give a good figure for body piercer, but know that there are those who make up to 60k a year. I would not say this is a good average though. You can find most of this research online by simply googling it, or by going into the places these respective individuals work. If you're courteous about it, they'll likely be glad to discuss it with you so long as they're not busy. Understand though that some people are sensitive about discussing how much they earn, so don't push the matter if they avoid that question.

Good luck in your search!