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Browse credit cards from a variety of issuers to see if there's a better card for you.
I believe the State Department FCU does not do an HP for a secured card. You might search SDFCU here on myfico.
I don't have any experience with them but Open Sky offers a secured Visa with no credit check. Does not report as secured and reports to all 3 bureaus. Minimum required is $200:
Who cares about inquiries for secured cards?
Other than an open judgement it's difficult to get denied.
I would worry more about finding cards that have the ability to graduate personally. By the time you have enough history on the secured cards to do you some good, the inquiries are not hurting your score much if at all anyway.
I have 15 inquiries. So yes I'm worried about any hard pulls to my credit score.
I agree about OpenSky and SDFCU being great and no credit check. Here in Seattle we have branches of Alaska USA Fed CU and they issue secured cards for any amount you want (without limit) with no credit check and they report to all three bureaus.
I would seriously do OpenSky, SDFCU and then call every credit union in your area, starting with the largest ones. Lots of CU's will give membership with a clear Chex and use the credit report for ID only (no hard), and then will issue a secured card with no credit check. You just have to make some phone calls.
Don't do what I did for a year and assume that they all operate the same way. This is not true at all. They each do their own thing and you are likely to find one that will work.