You will need either a cosigner or a job making a certain minimum salary and two years of credit history in order to get a private loan through Discover (I couldn't find a cosigner and had to eat the HP anyway).
The other side of things is that while student loans are good for your credit, the diversity that a card adds is, I think, totally worth it. My brother has had student loans for years, and he couldn't get a credit card (full disclosure: he's had one collection, and a few lates on his loans). The reason cited denying him is lack of credit mix. Which makes sense if you think about it, they measure different kinds of responsibility.
Good luck, in any case. 
Everyone's situation is different but from my personal experience Chase and Barclays would not accept SLs only as 'having credit'. They specifically stated rev cc's and Chase went further to say bank cards not store cards.
@Jungook wrote:
@sergi0wned wrote:There's a silver lining in everything!
I received a pre-qualified offer in the mail and was approved for a Discover It Student this summer after completing my first year of college and having my federal loans on my report for about 8 months. I also had 4 months worth of on time payments with my 1st Financial Bank USA Visa on my report, but other than that I had nothing.
I'm sure others will chime in, but I just wanted to share my experience in the hopes that it might help
Thank you for your input. How would I go about in receiving a pre-qualified offer? Do I sign up with Discover somehow?
It just showed up in my mailbox one day; I didn't do anything to get it. You could always sign up at https://www.optoutprescreen.com/ just to make sure that you're opted in to pre-qualification offers.
I think Discover has a pre-qualification site, but you probably won't have any offers until you have some more stuff on your credit history.