Yes, that’s the Amazon store card. It’s actually more like a line of credit, because all they send you is a paper card with your account number on it.
Yes, even though they are showing as paid you should try to get them deleted. You’ll be surprised how much your credit score will change after they are gone. Start sending those goodwill letters!
Check out this article about paid and unpaid debts: http://www.credit.com/credit_information/debt_help/Pay-for-Removal-Deals-Removing-Collection-Accounts-from-Your-Credit-Reports.jsp
Also, you can get your free annual credit report from: https://www.annualcreditreport.com/ (this is THE official website). They don’t give you a score, just the reports (though I think they give you the option to buy the score if you want). Find out how old those collections are. Try to find out what your FICO score is. FAKO and FICO can vary quite a bit sometimes.
With a 670 score you could probably get other unsecured cards, like the GE Amazon card I believe. It’s always wise to wait a few months between applications, specially if you don’t have other credit cards right now. Let your CapOne report, this by itself might raise your score if you don’t have other cards reporting. Give them 30-60 days to report your new card to the bureaus.
Some crazy people at the myFico forums for sure! Haha. I guess some people like collecting plastic.