No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
Removing baddies can only help your profile. You may get a small score ding if you are removing a tradeline that is your oldest one, but for the most part, getting negatives off only help. If it does not help right away it will down the road. If these are your only negatives then you should get a nice bump, if there are other ones still reporting then you may not get anything right away, but down the road, it will help your score to grow as other baddies are removed or age off.
If you will list out your accounts, with balances, credit limits along with any baddies you have such as lates, charge off, collections etc.. then someone will be able to predict what type of score improvement you may get from certain actions.