So, who do I write this check to?
Although it seems obvious, remember that you don't necessarily want to fork over funds to just anybody for the work they've provided. Paying a business -- as opposed to an individual -- usually provides some assurance that you're on the books somewhere.
Paying an individual opens some serious loopholes. If the contractor has a business license yet they're still asking for an individual check, it probably means that the contractor will not be reporting that income for taxes -- not exactly a sign of an honest worker. If they don't have a business license, you've now opened a whole can of worms. Not only are they unlicensed, but you're essentially putting yourself at liability for any badly done work (or worse, any injuries sustained by the workers).
In addition, you should never pay cash, which is impossible to track and is often requested by questionable contractors. Checks, loan financing and credit cards are typically much safer options.