Never move data from one server to another

I am in need of a Server expert to utilize their technical skills to help me with a project. The task is to move data from one server to another as I have purchased a new server. The data I am dealing with is operational in nature so it's very important at any cost, and the amount of the data which needs to be transferred is less than 5GB. The right applicant must be able to promise efficiency and accuracy in completing the job.