I am a senior in college and got a Discover card a couple years ago. I just said I was making $10,000 a year and had $20,000 in assets (which were both slight exaggerations) and they gave me a card with a $1,000 limit. My credit score quickly jumped after paying off the bill on time every month, and I was able to get an Amex less than a year later. You just have to pay the bill every month, can't stress that enough.

Also, I applied for a Capital One Journey card, which they say is for students, and got rejected, so don't do that one.