Yes, Davaoguy2, Jesus does have a beginning, Melchizedek

does not. But the Bible does not make it clear when was Jesus created. Some verses seem to say he was created before the world, other verses seem to say he was created inside Mary. But since there is no contradiction, we have to conclude we don't know. But I believe Jesus will explain to us all those verses and all other difficult verses when he returns.
Concerning your question of what does it mean that Christ is a priest of the order of Melchizedek, clearly Melchizedek established an order of priesthood, preceding the Aaronic priesthood and being superior to it. Melchizedek was the first priest of the order, and Jesus became another priest of the order. There is no evidence that the Melchizedek priesthood was hereditary, unlike the Aaronic priesthood.