I would discuss your budget with your parents using specifics schools and NPC numbers. Only after you and your parents have this discussion should you adjust your list. Strangers don’t have nearly enough insight into your parents priorities, finances and desires to give you definitive advice.
Talk to those that know you best and love you.
The school you attend and its reputation in finance (if we are talking IB, PE, VC, etc) will likely have a meaningful impact on your eventual opportunities and outcomes although of course exceptions exist.