As someone not living in the US and not seen much of the NCAA college football, I was wondering whether or not the athletes have to supply their own helmets as they get sprayed and painted the university's logo or do they just choose a helmet and the university provide it to them?
No , the athletes doesn't have to provide or supply their own helmets.
Universities also don't have to buy new helmets all the time and may paint over helmets they already have. And for those who have to buy new one collects money by reselling used one to donors. Not sure about choosing the helmet, many article's on NFL mention player can choose their helmet but found nothing about NCAA. University will buy the helmet and provide it to the athletes.
Source: CBS SPORTS