It would really depend what baddies you have now, how old they are, and what CCs you have already.
I'd save for a secured card somewhere if you don't have any cards. Focus also on cleaning up your reports. If you took a week and really hammered your reports, your scores would be in the 600 range before summer.
I have student loan baddies, 4 open credit card currently (4x300 CL) all with 0.00 balances. 2x30 days lates that are about 6 months old.
The recent lates are going to make it tough. Can you hold off until they go over one year? Otherwise, I would suggest a fully-secured card from a CU, which will give you an in for other products as well.
* Credit is a wonderful servant, but a terrible master. * Who's the boss --you or your credit? FICO's: EQ 781 - TU 793 - EX 779 (from PSECU) - Done credit hunting; having fun with credit gardening. - EQ 590 on 5/14/2007
You already have the card history, you are just stuck with low limits. I'd try for CLIs if you can. If not, and you still want a card, then I'd try a secured card with a higher limit ($750 - $1000 +)
If you keep applying, assuming you get that card, you have several thing that may go against you: 1) more inquiries, 2) likelihood of more $300 limits, 3) decreasing history, and 4) when your scores improve down the road, you'll be in worse shape to app for better cards. I mention all of this from experience anyway. I'm stuck with $300-$600 limits. On top of that, because of the newness of my credit, even with quasi-OK scores, I have been likely turned down for 4 card out of my last 4 apps (Citi, JCPennys, CCCU, and Penfed).
I like the site I found on here www.whogavemecredit.com and I looked at all the cards people were denied or approved for and was my final draw to try for orchard and I was approved from Orchard. Also recently on here just found out about the crown jewelers card where they don't check your credit and they have a rebuilding program
10/11/2017 EQ 640 TU 639 EX 652 12/10/2016 EQ 621 TU 607 EX 626 10/10/16 EQ566 TU591 EX 587 01/31/2008 EX 502 EQ 466 TU 481 3/14/2008 EX 578 EQ 539 TU 543 4/16/2008 EX 622 EQ 532 TU 578 5/19/2008 EX 604 EQ 591 TU 592 1/1/2009 EQ 625 EX 576 TU 569 02/13/2009 EQ 648 EX 617 TU 590 09/28/2009 EQ 568 TU 591 Thanks to all Fico supporters for your encouragement and advice