There's no question that the worse your driving or legal record looks, the harder it is going to be to find a truck driving job.
Most companies will have a specific policy regarding moving violations in a specific time frame, or require a specific amount of time to have passed since a felony or DUI conviction.
There are some companies that will not even consider applicants with DUI/DWI's or felonies, so generally drivers with an iffy past may need to dig deeper for their first driving job.
One other point to consider is that drivers with a DUI or felony may not be allowed to travel into Canada, further restricting their company options.
Most companies are going to have some kind of policy regarding a specific number of moving violations in a specific time frame, usually no more than 2, or 3, in the last 2 or 3 year period.
Additionally, any speeding tickets 15mph or over the speed limit will be considered reckless driving and may prevent some companies from hiring you altogether. The worse the ticket or accident, the harder it could make it to find a job.
Many companies will hire applicants with DUI or DWI conviction, and most will require a certain amount of time to have passed, and will usually still consider each applicant on a case-by-case basis, regardless.
Applicants that have been convicted of a DUI or DWI while CDL holders, or while operating a CMV that requires a CDL, face especially large hurdles, as the FMCSA has set specific disqualifications for those drivers.
As with DUI/DWI convictions, most companies will require a specific period of time to have passed since the felony conviction, and will take each applicant on a case-by-case basis.
The Department of Homeland Security requires drivers to undergo a background check and be cleared for the Hazmat endorsement, and the TSA provides a list of disqualifying offenses that would prevent drivers from getting it.
Certain offenses will result in a lifetime ban, while others require a certain period of time to have passed.