the DUI's will be a prob with any company, unfortunately. that long ago, i am surprised they are worried about it. before you go with a Swift or CRE (contract) see if you can get the $$$ together, or look at some education grants.
sense they are so old they should not be a problem. look for a truck school at a com. collage. they are the best. they cost about the same as 4 week schools but give you a lot more training and driving. when i went through, there was a guy with a dui in the last 3 years along with needing sr22 insurance at one time. he got in. so just look around. DO NOT go to a trucking company that has a truck school. you got to give them up to 1 year or else you will pay them for it.
2 guys from my class tried to get into central refer. they did not either. one had a great driving record too.
do not let it get you down.