First of all, congrats on graduating! I hope you can get a great job in the future!
As the previous post has said, unless you bank with Chase, they will mostly likely deny you for your first card. They like to see at least a year of experience, if I recall correctly.
Your best option would be to scrounge up the money for a BOA secured card. BOA is very generous with graduating and offering good CLIs once it does unsecure.
If you can't do that, since you are fresh out of school, I'd look into a local CU and establishing a relationship with them. They'll most likely start you off with a 500 unsecured card. CUs are more understanding and lenient, on most occasions, then the big banks. Although, you could ask who you bank with, they may have a credit card offering for you as well.
Why I don't recommend CapOne and Discover as your first cards, but your YMMV so consider that:
1.) CapOne will give you a high APR and often buckets people depending on when they applied (on experience, income, etc.) They do have the potential to grow, but it's slow. They do offer the ability to combine accounts should you try again and get a bigger SL on the second, but then you might end up with the old, high APR. Their secured card may or may not graduate.
2.) Discover often starts people with no credit with 500 and I've read anecdotes when they do that they are often stuck at that amount. Discover likes thin files and will give you your first card, but you are in a better position to apply when they are your second or third card. You'll get a much lower rate and a larger SL. They're a great company though, so, I wouldn't knock them off your list. You could try a Discover secured card, but there has been issues of it graduating, so, I'm leery to recommend this either.
As someone who has started with the CapOne Journey card as a current student, if I had to do it again, I'd definitely would have gone with BOA or a local CU instead. Or both! Treat it/them well for a year and that will open the doors for a Freedom. Best luck to you! 
