I don't think there is any right answer. If you're credit challenged I would apply for a secured card first. Some banks are tougher than others. If you do a search, you should be able to discover which cards are easier to qualify for than others.
One caution: Unless you are certain you will make all your payments on time, etc., some banks will treat default on one obligation as a default on all others. In that case, it is certainly better not to have your credit cards associated with other loans. Additionally, because of the bank’s right of set-off, credit challenged holders should not hold credit cards issued by the bank where they have deposits.
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I don't think it matters where the card is from as far as rebuilding your credit. What matters is what kind of credit terms are being offered. Some links you might find useful: http://www.consumer.ftc.gov/articles/0332-credit-debit-and-charge-cards
The one thing that concerns is that Credit Unions stick in these ugly cross-collaterization clauses so I would generally stay away from them if you have a car loan or mortgage with them, but of course this is only a problem if you overextend yourself.
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