@celluloid17 wrote:I don't know about minimum scores needed for these, but I would maybe aim for these three:
1. Bank Americard Travel Rewards Visa Signature - 1.5 points for every $1 spent used towards travel purchases and No AF, No FTF, EMV chip OR Merrill + Visa Siganture - 1 % back and No AF, No FTF, EMV chip
2. Fidelity Amex - this is not a Centurion backed Amex, but rather FIA (Bank of America) and it will get you 2% back on all general spend that can be deposited into a free Fidelity Cash Management account and then transferred to your external bank account.
3. Sallie Mae Barclaycard World MasterCard - 5% back on $250 a month on gas and groceries each, 5% back on $750 a month on Amazon, and 1% on everything else
Thanks, I will look into more info about these cards. Specially the first one 
@takeshi74 wrote:More info would help as best is always a highly subjective matter. What are your major spend categories? How much spend are you looking to put on your cards? Generally speaking, cash back may be better for lower amounts of spend.
@Anonymous wrote:I do NOT need to be in the Amex family (it's just not appealing to me).
You don't have any spend that qualifies for increased rewards offered on any of their products? I personally find the 6% back on groceries from my BCP to be very beneficial.
Backdating wouldn't benefit you? I added 2 new AmEx cards to my wallet last year. Since my MSD is in 1998 they both report as 16 year old tradelines.
The 3x CLI wouldn't benefit you? You state in your OP that you would like "great increases over time".
It would help with recommendations to understand why you're AmEx averse as you are ruling options that could be suited to you.
@Anonymous wrote:If you have any suggestions, please let me know and what the minimum score you believe to be approved for the cards.
Keep in mind that it's never just a matter of score. Your entire credit picture matters and what a specific creditor is looking for or looking at can vary.
thanks for the response! what I mean by 'generous increase overtime' is that if I need to request an increase i would like to see a few thousands increase instead of a couple hundreds. Personally, I don't want a credit limit more than $10,000 because too much credit can get out of hand sometimes. I pay everything in full every month and I try to live on my means. For example, if I can't pay in full at the end of the month then I just don't buy it. Huge exception for the car loan and future home loan of course .
i am focusing on travel rewards because my husband and I travel very often in different airlines ( most are delta, AA and united). We travel as much as we can. It would be nice to start collecting rewards on the paid tickets. I often pay for my parents tickets to come and visit once or twice a year from south America + all of my basic bills (phone, grocery, gas, insurance and so on) which is paid in full at the end of the month. Our major spending would easily be travel which will increase due to our move so we'll be paying my in-laws tickets to visit too. This is just our thing...we like to take care of travel arrangements for our parents.
I am not averse to Amex, is just my personall choice. If I had to choose 3 cards...I would have 1 Visa, 1 Discover and 1 MasterCard. That's just my personal preference. Low apr and low AF or no AF it's best. Personally for me 3 cards it's perfect...more than that I would just be asking for trouble 
. My view could change in the future but for now, that is where I stand. Oh, and I am rebuilding from medical bills. Got very sick and had no health insurance. Cleaning up my credit report now that I am more stable mentally and financially.