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.
I am licensed in California only and my answers on Avvo assume California law. Answers provided by me are for general information only. They are not legal advice. Answers must not be relied upon. Legal advice must be based on the interplay between specific exact facts and the law. This forum does not allow for the discussion of that interplay. My answer to any specific question would likely be different if that interplay were explored during an attorney-client relationship. I provide legal advice during the course of an attorney-client relationship only. The exchange of information through this forum does not establish such a relationship. That relationship is established only by personal and direct consultation with me followed by the execution of a written attorney-client agreement signed by each of us. The communications on this website are not privileged or confidential and I assume no duty to anyone by my participation on Avvo or because I have answered or commented on a question. All legal proceedings involve deadlines and time limiting statutes. So that legal rights are not lost for failure to timely take appropriate action and because I do not provide legal advice in answer to any question, if you are an interested party you should promptly and personally consult with an attorney for legal advice. Also, see Avvo's terms and conditions of use, specifically item 9, incorporated by this reference
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.
I am not YOUR lawyer. Don't rely on answers to questions as legal advice. For legal advice contact a Bankruptcy Attorney for a consultation. Tokarska Law Center is a Federal Debt Relief Agency representing individuals and businesses in filing for bankrutpcy protection under the U.S. Bankrutpcy Code. Kathryn U. Tokarska is a San Diego Bankruptcy Attorney, owner of Tokarska Law Center, 185 West F Street #100, San Diego, CA 92101, (619) 285-1992 www.sdbankrupt.com