VCs typically have experience working at, growing and/or selling a successful startup. I would almost say startup experience is essential in this environment since you've got to understand and relate to the challenges of the companies that you're looking to invest capital in.
You also need a strong understanding of corporate finance, deal structure and overall business acumen. You also have to network and hustle like crazy as there are plenty of other people who want to give money to businesses they believe will be successful.
It's pretty unheard of to move directly out of college into a VC role. You'd likely be building up a portfolio of experiences at other similar roles before moving into that world.
Most VCs typically start by getting a "pedigree" of sorts by working for an extremely well known investment banking or consulting firm. Most of these firms pull people out of the top ivy league schools or top of the class from non-ivys. They can be extremely selective because there is an unreal amount of competition that exists for these jobs.
Once people put in a few years of extremely challenging work at one of these firms, they hopefully have built the experience and networks that will allow them to move into the more nuanced world of private finance. So study hard and start networking if you really want to pursue that path...
Regardless of your path prior to the industry, there are really four main disciplines involved in venture capital, the importance of which ebb and flow over the course of your career as an investor. They are:
1) Prospecting/sourcing/finding deals: sales can be a great background for this, as can research. It is key to have an informed point of view as to where the puck is headed.
2) "Diligencing" deals - i.e., performing due diligence and asking the key questions of management teams about their company's prospects
3) "Selling into deals" - i.e., convincing founders to work with your firm as opposed to any other.
4) Adding value post close - i.e., finding ways to help accelerate the chosen company's path to a successful exit.
The reality is that many, many careers (consulting, journalism, medicine) can be great preparation for entering venture capital. What most firms will seek in hiring are classically important personality traits such as self awareness, drive, strategic thinking, and empathy. It ca be a very fulfilling career if approached well.