as long as you stay under the "magical" 26001 pound GCVW you do not need a "CDL", your class c will carry you just fine as long as your not doing this for hire. If you do plan on being for hire or commercial use, I would go ahead and get the class "B" for insurance purposes.
Also keep this in mind, as your gross weight goes up your braking capacity decreases. I tell poeple that get a new trailer to load it to capacity then find a good long parking lot in the middle of the night, get it up to about 50 mph and do a both feet on the peddles panic stop. You will learn will real quick your driving abilities, the lack of stopping power your truck has, and how tightly your butt can grab fabric!
Every one always wants to know how much they can pull, but the real question is how much weight can they stop if a kid darts out in front of them or traffic comes to an abrupt stop!
2 cents worth from a truck driver.