Which version of vCenter Server should I use for my ESXi 5.1 Build 799733 Host?
You can use vCenter 5.1 or vCenter 5.1 U1 to manage the ESXi host . Make a practise to check the VMware Prodcut Interoperability Matrix to check the product compatiabillity
I have noted that vCenter Server 5.1 U1 has been released about a week ago but not sure if the company would want to install something this new into the production environment.
Read the, whats new, release fixes and known issue of both the release and choose the one which you feel is better