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If its been at least 6 months since you last opened/applied for Capital One account, I would opt for the Capital One card. If you still want the Discover secured card as a way in with Discover and potential to graduate, I would do both applications.
Try to stay away from disco for now. Get your scores and limits up then go for it. As mentioned holding off 6 months will be greatly beneficial. Do you have more specific data points? 3 scores, # of inq, total accounts
Take the NFCU secure card and stay away from applications for 6 months to a year. Are the loans in deferment or repayment? Depending on the balance that contributes to util. and your denial letter will say something like “proportion of loan balance to loan amount is too high”. NFCU will become a revolver after 6 months or so if not request it. Then you can gradually work on CLI then go for others once scores reach 680-700 range. Pay in full the statement balance on the due date and charge $5-10 day or two before statement closing so you have low uti and carry a small balance. Good luck! Let us know of any developments.
Take the Discover approval. Then wait for the six months to a year to allow some of your HP to age. Plus just after the six month or so mark, your Disocver may graduate to a non secured.
Disco as mentioned repeatedly throughout the forum has a variety of unknown criteria for credit line increases. Some ppl they love and give legitimate increases to and some (specially the student and secured groups) are often restricted the ability to grow credit limits which is imperative to credit rebuilding and attracting premium lenders. There are no data points to support successful cli with Disco, but NFCU has a history of extending generous limits to its members.
Thinking take the NFCU secured... wait a few months.. (revisit this idea at 3 (check your scores and try for a preapproval) but consider waiting at least 6 mo) and then try for an unsecured student Discover... Regardless if you haven't already... and still want to get the Disco at some point.. sign up for Discovers free Credit Scorecard and get at least one real FICO per month AND put you on their radar..... and you can do that now =)