2 answers
Katy’s Answer
Short answer: it doesn't.
The long answer is a little more complicated.
There is a reason Ivy League schools are impressive: they've been around a very long time, and they produce some of the best minds in their field. Generally, this has to do with rigorous curricula, having the best professors, a lot of resources, and the prestige that comes with the diploma. Now, that isn't to say that the experience you get at an Ivy League school is actually going to be any better for you than it will from going to a state or community college. In truth, what you get out of your education comes down entirely to you.
Every school has its merits, and each program will differ school to school. The most important thing to think about when deciding on the school you want to go to is the reasons you are going to school. Are you going because you want to get the absolute best education and have the best experience during school? Are you going so you can get that piece of paper that says you have a degree and nothing more? Are you going to learn some, but to mainly find contacts to help you in your career? Are you trying to get a good degree without going into $100,000 in debt? Everyone's answer will be different, and should determine which school they attend.
For me, I got my Bachelor's at the college 10 miles from my house. It was generally frowned upon as the commuter school and the easy school because everyone could get in, and most people from our high schools could go there. The thing for me was that I wanted to live at home, I didn't want to go into a lot of debt for school, and it had the program that I wanted to go into, where most other schools didn't. I didn't see any value in paying a lot more money for my degree. I enjoyed my time at my school, and I think I had a lot of great professors that really taught me more than my class subjects. It was a good school, but not prestigious, yet. Today, when I mention my Alma Mater, most people don't know where it is, or what I'm talking about, and that doesn't bother me one bit. It bothers some people.
I will say, though, what truly matters about a school is it's programming and student support. If you can find a good state school with low tuition and fees, the major you want, is ranked well among similar schools, and has decent support staff and professors, you should be just as well off there as anywhere else. The only real-world benefit to attending a major school is the networking opportunities, and the ability to name-drop for shock value. If you want to live your life saying "I went to Harvard", then you might want to consider going to a major school, but if that doesn't matter one whit to you, then you can get just as good an education at a local state college.
Justin’s Answer
The long-and-short of it is that you may never know it's the "right" path while in the middle of making it happen. But you CAN tell if it's worthwhile by simply assessing yourself and how engaged you are in the education/work. You will not enjoy every class or the daily grind to pay the bills, but if you, overall, find yourself staying interested in whatever field it is you get into, then that's a sign that things are generally good. Maybe better than asking about the "right" path is to define the "wrong" path. In my opinion, the wrong path is becoming disinterested, disengaged, and not attempting to figure out what it is you ARE interested in. It's perfectly normal to ask, "When am I ever going to use this?" on occasion, but if you're constantly asking yourself that: wrong path.
Paths change, careers change, and uncertainty & evolution are part of the process. It's apathy and indifference you need gauge in order to at least know if you're on the "wrong" path. And, frankly, it's better to be uncertain but engaged in education and work in which you thrive than to be on a certain path which makes you want to run headfirst into a brick wall.
I started in engineering at a major university (Texas A&M) known for its engineering program, driven moreso by wanting to satisfy parental expectations than by a genuine interest in engineering. I quickly became disinterested, disengaged, and really fell off the boat for a while with both school and the idea of a career. I eventually went back to Tx A&M, and finished with a BSc. Economics degree in 2010. It was a TERRRRRRRRIBLE time to be an economics major (housing/banking crisis, global economic recession, the End of Times, four horsemen/pale riders..., etc...). A professor, first day of class in 2009, began by saying , "This course is utterly irrelevant right now. But maybe it will mean something again someday. Oh yeah, and my name is professor..." Clearly, that cast a shadow on my prospective career. I left school, started working as an engineering-designer to pay the bills, and eventually got into finance after going back to school for a MSc. Finance degree. One morning in 2008, after getting back into A&M, I woke up and almost decided to quit school, get certified in welding and just do that for my 9-to-5. I enjoy what I do now, but in all honesty, I think I could've been just as happy being a welder. Hell, sometimes I still think about quitting business valuation to get certified in some spark & arc. I'm big on education, but I will say that sometimes the best educational path means not assuming that a 4-year (or beyond) degree is your only choice.