All (and hellesangels)
I answered my own question regarding which SATA ports to use to on the Gigabyte GA-Z77X-UD5H motherboard.
The internal gray ports are the SATA ports on the Marvell 88SE9172 controllers. There are three. Two are in the stacked bank of SATA ports, and one is along the edge of the motherboard. They are all gray colored. They are all SATA III (6.0 Gbit/s).
The white port contains two SATA III (6.0 Gbit/s) ports on the Intel Z77 chipset controller.
The four remaining black ports are all SATA II (3.0 Gbit/s) ports on the Intel Z77 chipset controller.
I used a white connector Intel SATA III port (6.0 Gbit/s) for my SSD drive and a black connector Intel SATA II port (3.0 Gbit/s) for the optical DVD-ROM drive. Things are working fine now. ESXi 5 saw the drive and installed to it without a problem. The installer apparently could not see the hard disk when it was attached to the Marvell controller ports, so I am led to believe that there is no Marvell controller driver resident on the ESXi 5 installation ISO.
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I have been looking for a VMWare driver for the embedded Qualcomm Atheros AR8151 NIC. I still have not found anything, but in the meantime I am up and running using the Intel 82579V NIC also embedded on the motherboard.
If network throughput becomes an isue using only one NIC, I may investigate using a PCI slot-based NIC to add additional throughput. Not sure if I will need to do that though as this is a machine that I am only using for personal training purposes. So far networking is fine in and out of 8 lightly used VMs.