It really depends on which part of cartilage your daughter is getting pierced? It should be a needle not a gun for a piercing such as a cartilage.
I have 3 cartilage piercings and one was not sore and the other two were sore then more painful afterwards. Especially when they are knocked.
The one thing to remember with them they are not like normal skin piercings and that they can take up to a year to heal and to not over clean them.
My method of cleaning is a Tea spoon of salt to a pint of boiling water and stir well, wait till it cools and generally I use a cotton bud to clean properly into it.
I made the mistake of cleaning it and it took longer. With my recent piercing I cleaned it out when it was sore or feeling the build up, other wise I rinsed it in the shower in the mornings and this one has healed better and quicker.
Numbing it isn't something I would recommend as someone said it would tense the skin. The best thing to do is not tense yourself, relax and breathe.
Take juice and something sweet as sometimes people can feel a bit light headed afterwards (especially if it's their first piercing) and this helps stave this off.
Jewellery wise you won't normally get a nice bar (depending on area) if it's a thicker part as you get a bigger bar which is changed down (the piercer will tell you when to come back) then you tend to get nicer bars and balls. Unless it's outer ear you get more of a choice.
Hope this helps and makes sense as I know I've jumbled and rambled on lol. My experience comes from a long time of working in piercing and tattoo shops and having them done myself. Any issues or question feel free to message me