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If building your score is the goal, I agree with your TU only focus, but wouldn't go near Barclays for a while yet.
How do you feel about Walmart? Free TU08 score with paperless billing, and the credit limit can grow very quickly...they are TU pullers as well...
Good luck with Walmart/discover ,I don't want to be an Debbie downer but Walmart doesn't pull same tu fico as one you get here. I learned that hard way.my myfico tu and Walmart tu differ by over 100 points .