Part of the trouble is that "normal" SATA controllers sometimes include features that are REQUIRED in true eSATA, and sometimes don't, and it is hard to figure that out. So sometimes using a simple conversion connector that allows you to plug an eSATA external case into a mobo SATA port works OK, sometimes not.
In your case, the mobo manual offers a good solution, I think. It says clearly that there are two SATA controllers - one is by Intel in the Southbridge chip, and it controls six ports in a group labeled "SATA2_0" though "SATA2_5". The other is a Gigabyte controller chip that handles two additional ports right at the end of the RAM slots in a separate group labeled "GSATA2_0" and "GSATA2_1". Each controller chip can be configured separately. The manual also says that each can support hot swapping if it is set to AHCI mode. The trouble is that Windows does not know natively how to handle AHCI, so you have to install the AHCI driver to get that to be able to use a port in this mode. However, if you do that you have a lot of trouble trying to install Windows in the first place, because you have to install the AHCI driver at the start so Windows can access that drive for installation.
I think there's a good way around these restrictions. You set up the main Intel controller NOT to use AHCI and hook up your regular internal SATA drives to it, and install to one of those. Then you set the second (Gigabyte) controller to use AHCI on its ports only and install the AHCI driver into Windows. You hook up your external eSATA drive to the Gigabyte chip-controlled SATA port only, and voila!
You said you want to use a "typical SATA hard drive as a portable drive that I can use to transfer files, etc...". Buy an external drive case that has two features: (a) it accepts a regular internal SATAII drive; and (b) it has at least an eSATA port on the outside (I'd also want a USB2 port, too, for ease of use on other machines). Most actually come with an adapter cable that plugs into a regular mobo SATA port (remember to use the GSATA2_0 in this case - note the "G" at the front) and ends in an eSATA connector mounted in a plate that mounts on the back side of the case like a PCI card. Then you use an eSATA cable to connect from that to the external case.
Now some BIOS details. In your manual, pages 52-53 about the BIOS pages under "Integrated Peripherals", set the "SATA RAID/AHCI Mode" to Disabled, which is the default. Now all six of the SATA ports this controller handles will behave like traditional IDE ports in terms of what Windows sees. On the next line, set "SATA Port0-3 Native Mode" to Enabled. With these two settings, the mobo will make Windows think that it is dealing with simple IDE drives, and Windows already has built in all the info it needs for this. So you can install the OS with no trouble at all to any drive on these ports - probably you put your C: drive you boot from on port SATA2_0.
After you install Windows, go back into BIOS and see manual page 55. Back in "Integrated Peripherals" again, set "Onboard SATA/IDE Device (GIGABYTE SATA2 Chip)" to Enabled (default) to get that chip's ports working. On the next line set "Onboard SATA/IDE Ctrl Mode" to "AHCI" to enable, among other things, hot swapping support on these two ports. Save and exit to boot your system, then go to manual page 65 and use the CD that came with the mobo to install all the required mobo chipset drivers. That process ought to install the AHCI drivers so that feature can be used by Windows on the two SATA ports controlled by the Gigabyte chip.