Who should I try to get a job with ?

I have about 10 months exp running a tanker. I have no dry van exp and my tanker didn't even have a 5th wheel ( it was a pup with a pindel hook ). I talked to JB Hunt the other day and he said if I had at least 6 months within the last year he could get me an otr position at .35 a mile averaging 2300 miles a week 12 days out 2 days in. I would like to run long haul and have been in the trucking business for the past 23 years all but 10 months in a straight truck. I was thinking it would be a good idea for me to go out with a trainer for awhile. Which companys should I try ? I was thinking about Shneider, but they told me I live to far from their terminals ( Huston or Dallas ) I do have a local job that pays well when we are busy, but I have no health insurance, so I don't need a new job today. Also it was a year ago this month since the last time I drove a class a truck.