I would go directly through the state as this would usually save you money. However, business brokers such as LegalZoom can have their advantages also, like having a registered agent through them (one that is an attorney). I recommend you do some research and also contact your secretary of state's and county clerk's office for more information on filing for an LLC, Corp or DBA.
Also, remember you will be paying more if you go through Legalzoom or a similar system. Both options have their perks (going via state saves money) and Legal zoom, as HostLeet said, have registered agents. Look at your options, research, and come to a system that fits your situation!