Choosing the right piercer is totally key here.
It’s definately better if they have it done with a needle rather than a gun - because of the fast action of the gun, there is more chance of contamination, while a proper studio will be able to autoclave and disinfect their equipment to ensure sterility. I would also expect that a fresh needle will be used - you want to see them open the sterile packaging in front of you etc.
The pain’s not that bad - a good piercer will go through breathing techniques with you which help you prepare for it - but yes, it will hurt a little. About the same as ears I think.
Make sure they keep up with the cleaning regieme as recommended by the piercer, and don’t change the jewellery until the wound is healed. There are special studs for the nose which have a small lump at the end to help it stop falling out. The stud you get when first pierced is likely to be bigger than what you would wear normally, as the nose will swell a little, and you want to make a big enough hole.
The stud can get a little annoying - that’s why I eventually took mine out - it catches on things (towels at the gym etc), and can be pushed out a little if you touch your nose etc, so you do have a constant maintenance thing going on - can be a pain. Also, worth bearing in mind that the hole will never completely close over - I took mine out after 5 years in 02, and you can still see the hole (although it’s closed up enough that I can’t get jewellery back in). So it’s not a totally reversible decision. But as long as they are OK with that, not a big risk.
Only other point to consider is that at some point it may be considered inappropriate depending on where they end up working - but they are young enough to enjoy it for a while before having to deal with that. I really loved mine, but did take it out for work (corporate environment) but don’t miss it now - replaced with a more discrete tragus piercing.