Chicken and the Egg story
Some people recommend credit unions as they tend to be very flexible. Others will recommend a secured card that will graduate into an unsecured card. More still will recommend paying cash for everything (I kid).
Here are some options.
1 - Ask your parents if they would be willing to open a joint credit card account with you (assuming they have decent credit). They can keep the card(s) if they wish. You just want the history.
2 - Ask your parents if they can add you as an authorized user (AU). Same caveats as above.
3 - There are a few decent student cards out there you may qualify for. The Citi Student Thank you card has 5x TY points for dining out which is good. Discover may also give you a shot at their student card too.
4 - Try calling the recon number again and ask them if they might approve you for the Freedom card and emphasize that you are looking to build a relationship with a bank, not apply to garbage that you need like a hole in the head.