I've never had a secured card so unfortunately I can't speak from first hand experience, but I've heard Capital One has some very reasonable secured cards. I also think there's a secured version of the Discover It card available, that may even graduate to an unsecured card after a period of time (sorry I can't be more specific, maybe 6-12 months?). I'd probably go with that one personally because the Discover It is a great card!
If you have access to a credit union they might have good secured cards available.
Main companies to avoid: Credit One, First Premier.
My advice would be to Google "Best Secured Card" (and maybe also "Worst Secured Card" so you know what to avoid) and research them a bit from several blogs and sites. A preliminary search for that indicates that some of the best are:
-Navy Federal Credit Union Rewards Secured Card
-SDFCU Savings Secured Visa Platinum Card
-USAA Secured Credit Cards
-Discover it Secured Credit Card
-Capital One Secured MasterCard Credit Card
I'm not recommending these personally because I really don't know firsthand, but they're probably worth researching further. Sorry I couldn't be more helpful.
Anyway, welcome to the forum and good luck with your credit journey!