I'm not an expert, but it could depend on the CCC and/or the amount of the charge offs, etc. I had assumed the worst as well as I rebuilt and figured I would have to avoid CCCs with whom I had had questionable past. I had a $300 CL Capital One card back in (roughly 2004/2005) and it grew to about $700 ($400 over limit) and was charged off. I ended up paying the collection in full.
I just applied a couple of weeks ago for a Capital One Platinum MC and was approved with scores in the mid-600s. Credit line was surprising $3000 and no AF.
So I guess my point is, it's possible that Capital One doesn't hold it against past offenders if the scores are in their comfort zone. OR, it's possible that the fact that my charge off was <$1000 was less offensive to them.
I would say you should decide on the card(s) that seem best suited for you and give them a shot, regardless of the past history. But that's just me based on my limited (positive) experience.
I don't think you should wait to apply until your report is completely clean--if your worst baddies have dropped off completely, and your others are over 2 years, most card companies will consider you. There are some who apparently hold grudges, but I think most do not have long memories.
With credit tightening, if you wait around, you might not get credit at all. If you get at least one card, it will boost your score as soon as it starts reporting--my scores jumped 35 points the first month I showed use of a card and my scores are all worse than yours (660s).
I have a Cap One and a BoA partially secured, both of which I recommend. I also have an Orchard, but they suck.