If your Gross weight and the vehicles GVW is under 26,001 lbs and your trailer (if you pull one?) has a GVW of under 10,001 lbs no CDL is required. Your equipment GVW and your loaded gross weight cannot exceed 26,001 lb.
Keep in mind, If the vehicle your planning on running (obviuosly a hotshot style set up) has no air brakes, you haul no hazmat,, don't pull doubles or tripples the CDL is very easy for a guy to get. You can actually take the test in the vehicle or cobination of vehicles you'll be driving. Stepping up to even 36,000 gross weight with a CDL will allow you to earn a much higher income.
As far as having a DUI on your record. If it's over 10 years old it probably won't make a difference. I think 10 years is as far back as Insurance Companies and Carriers even look?
When your a Independent and Brokers are checking you out they'll look at your Insurance, FMCSA info, and your www.safersys.com report. Pretty much anything about your company they can find. They don't check your personal driving record. They figure if you have all the right stuff you are approved by the Department Of Transportation to run loads.
If your thinking about leasing onto a company do yourself a favor and type that companies name into the search bar at the top right corner of this page. See what kind of comments have been made about that company. There's a ton of old post about companies that could help you avoid making a bad decision. Good Luck.