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I just checked the Discover site for pre-approvals.
Don't they know I'm in garden mode‽
When I read adult, I thought you wanted the new Playboy World MasterCard or something Good luck on your new apps.
AMEX also has a pre-approval you can check if you are interested in them.
When I applied for AMEX Clear, I only had 3 cards:
US Bank - 2-3 years old
Citi Platinum Select - about a year old
J.Crew - about 2 years old.
AMEX approved me for a $2k limit (my score was 715 iirc)
I applied for Chase Freedom a few weeks after AMEX and got approved with a $4k limit.
You might be able to get a nice prime card with your score.
I would try for Barclays. They have many cards to choose from and tend to give out decent CLs (you can even try to increase the CL during activation) and CLIs.