Single Member LLCs are considered Sole Proprietors. You are not a employee of your LLC, but rather self employed. You can not pay yourself salary and issue yourself a W2 either. You do draws from your LLC. To the point you hire a 2nd person, he or she will be considered an employee and you will need to have WC. WC rates also vary from state to state and also depends on the nature of the work the employee is doing.
State laws vary -- in Texas you would not be required to carry workers comp, but not having it for that one employee would open you up to unlimited liability for any on-the-job injury. You'd also lose certain common-law defenses, for instance, the ability to argue that the worker's negligence caused his/her injury. So that's one reason to carry it.
Your profile indicates that you are in South Carolina where it appears that workers' comp is compulsory only if you have four or more full or part time employees -- so you might check into that with your commission there or with a local attorney to see if you really are required to carry it.
Not sure about South Carolina but if you are self employed with no employess and don't pay yourself via payroll, then you don't need to pay workers comp. However if you pay yourself via payroll, then you'll have to pay payroll taxes on the money you pay yourself as well as comp because you are then considered an employee of the company.