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The Best Buy store card is a fairly typical store card. You get 2.5 points for every dollar spent at Best Buy and redeem the points in the form of a $5 voucher for every 250 points spent. You can opt for special no interest financing and the term depends on the price. However you have to chose between special financing or points - you can't do both.
Citi Double Cash is one of the best cash rewards cards on the market today. The reward structure is a little unique in that you get 1% cash back at the time of purchase and 1% when you pay the balance for an effective 2% cash back. There is no annual fee but there is a quite high (3%) foreign transaction fee, so I wouldn't recommend using this card when you're traveling internationally.
The J.Crew store card is a good card to have if you frequently shop at J.Crew. You get 1 point per dollar spent which is ok but nothing special. However you also get free alterations and earn bonuses on large purchases. Right now you get $25 for $500 in purchases. This card is really only useful for frequent J.Crew shoppers and especially those who take advantage of alterations.
The Amazon store card is a mixed bag. It offers 5% back on all Amazon purchases which is great, especially for people who frequently shop on Amazon. However the bank which issues the card, Synchrony credit, can be a pain to deal with. Their website is mediocre at best and it often simply doesn't work. Don't wait until the last day to make your payment because their website is not reliable at all. Great cashback, bad bank.
Bank Americard Cash Rewards is a great rewards card to have in your wallet. It offers 3% cash back on gas, 2% on groceries and 1% on general purchases. The gas and grocery rewards are excellent, although I use other cards for general spending. In addition to the cash back rewards, you get an extra 10% by depositing the cash back into a Bank of America checking account. Bank Americard Cash Rewards has no annual fee.
I am in the process of rebuilding my credit and was excited to receive a pre-approval to apply for the American Express Green Card. The Green Card frankly isn't a great card, but it does get you in the door with Amex. You get 1 bonus point for each dollar of spend which roughly translates to 1% back but it depends on how you redeem it. The annual fee of $39 is expensive for a card without great benefits but hopefully after responsible use you will be able to get one of the better cards offered by Amex.
The Capital One Quicksilver card is one of the best rewards cards on the market. It offers 1.5% cash back on all purchases. There are no catches or gimmicks to the cash back, you can easily redeem your cashback as a statement credit or opt for a gift card or check. There are other cards offering better rewards for certain categories, but for overall spending, the Quicksilver is probably the best rewards card.
The American Express Blue Cash Everyday card is a nice rewards card for gas and groceries. It earns 3% cash back on groceries and 2% on gas. All other purchases earn the default 1% so there are definitely better rewards cards for those purchases. However gas and groceries account for a lot of my spending (and I'm sure most other people as well) so the card is worthwhile to have for just those two categories. For all other purchases I use other cards which a higher rewards percentage.