Umm it depends on what you're able to afford. if you can afford to not live in newark, then you may be happier living elsewhere (not so much because of safety but more in terms of quality of life).
a lot of people in their 20s/30s live in Hoboken and commute to Manhattan to save money, but I'm not sure how much money they actually save because Hoboken is really up and coming. That being said, you could also find an apartment in other nearby towns in North Jersey and commute to Newark for school (with a car or without--Amtrak and NJ Transit both stop in Newark, and there are also buses I'm sure) while still having the benefits of the city (New York) for a culturally-enriching social life. Having grown up in North Jersey, I can vouch for the public transportation into the city from the suburbs as being top-notch.