Research some more.
I suggest you go to www.classadrivers.com/truckingcompanies.php and see the company policy for DUI, DWI, accidents, tickets, felony convictions and, in your case, age requirement. You should also do a search on the layover message board for the companies you are interested in. For example: CR England is not talked about favorable here.
Clean driving and police records are definite pluses. 5 jobs in 3 years could require an explanation. Because of the high number of applicants, companies just don't take anyone.