The weird thing is that if you use the credit impact simulators with the credit monitoring services, they show that the impact of paying your credit cards off completely is more negative than carrying a small balance, which doesn't make a great deal of sense, one would think. From what I can gather, the rationale is that carrying a small balance shows you making payments over time, as opposed to having a zero balance. This doesn't quite compute with me, but I don't truly understand the inner workings of the scoring models. To confirm this, I used simulators with both TransUnion and Experian, and both showed this. I know that it's easy to find people on both sides of this argument, so I can't say which is the best option (certainly whichever side someone falls on is the one they'll argue is the right one! chuckle).
In all fairness, your best tool is time. The effects of your prior bad decisions will lessen over time as they move further away in your history and then disappear altogether. Obtaining a credit card just because you think you need one is not a compelling argument, by any means. If you can't rationalize reasons why you need it then maybe you should question the wisdom of such a decision. If you don't have a particular need for better credit right now, why be in a hurry to take on debt?
Whatever the formulas are for calculating credit scores, the specific details are a pretty closely-guarded secret (they're proprietary for starters, plus it theoretically prevents people from "gaming the system" for a better score), but if you do enough research online, you can get a pretty good sense of how they work in general.
Whatever you do with your credit should be in line with your overall financial goals. If you want to remain debt-free (at least for now) then having a credit card you can't otherwise justify a need for just introduces temptations which could prove tough to resist ("wants" quickly turn into "needs" when you can put it on a card you pay later), then you're right back in the same place you were earlier in your life.
Instead of trying to figure out the "best strategy" for a credit card, first ask yourself how necessary it is to you right now in light of your financial objectives, then go from there.
I hope this helps.