The good news is that getting your license pulled for administrative reasons (as opposed to reckless/DUI/test refusal) is not an issue with the FAA. You may have to report it on your medical, depending on how the question is worded, but they will not care once they know it was for lack of insurance.

So basically as far as motor vehicle actions you have a couple of speeding tickets. Not a big deal, but don't get any more.

Your financial problems are another story. Airlines generally do look at that sort of thing. Some recruiters might have some sympathy for your circumstances due to the state of the economy and the aviation industry, but I would not bet on it.

The bad news is that when airline hiring resumes, there will be a large pool of qualified applicants with clean records. You might have to wait a while until things become less competitive.

As far as 91 and 135, they will generally be less strict than the airlines, especially part 91. I even know of one guy who prefers to hire pilots with a DUI because he knows they will stick around longer. The best 91 jobs will probably be every bit as strict as airlines, even more so.