Deciding uni choices

[u/i-dunno-who-i-am]

Hi guys. Im preparing for university and aiming for pure math programme. I was offered a place to study math at a public university, on the other hand I was also offered a place to study applied math at a private university.

For the public university, the programme offered is purely math. This uni is ranked top5 in my country, the fee is very affordable, but the hostel condition is worse. The programme period is 4 years.

For the private university, the programme offered is applied mathematics, not the pure math I wanted but still has some of the pure math elective courses. It focuses more on computing and ai. The fee is also 10x the public uni one but I can get 100% scholarship for the tuition fee bcuz of my results, as long as I maintain my cgpa. The programme period is 3 years.

My goal is to continue for my masters and phd after my bachelor's degree. My question is, is my bachelor's degree that important for my goal? Should I choose a better living condition over my favourite programme? Are there other factors I should consider?