My answer 6 mo ago would be different than today !
The first thing you need to do is pull your reports - go to annual credit report.com. When I pulled mine 6 mo ago I was shocked - I thought they would be horrible horrible. Wrong! My scores were in the very low 600's. I worked on them for several months - I disputed some things and a few were deleted and my scores jumped to around 640. With that - I got several new CC's, a used car loan at a subprime rate (10% - but I have seen worse AND I did have a redeemed repo) and got limits on my existing cards increased. It was a pretty sight.
Enough about me. but seriously, you have to pull your reports and check your scores so you
know exactly what you are working with.
To improve your score you need to decrease your utilization to less than 30% (much less is better) and see if any of those baddies can be disputed. Once you do that, and your score climbs over 600, you may be able to get some of the easy cards. But remember everyone is tightening up so it may be awhile before you can add to your collection. Never ever be late on the cards you do have. 1 30 day late will set you back big time.
Make a budget to get those cards paid down and that will be the quickest way to see your score increase. The old bad accts could keep you from getting new credit, but you can work on those by checking the SOL and disputing errors.