Get updated drivers from Gigabyte's website for your motherboard - don't install off of the CD if at all possible.
Same for GPU, but go directly to nVidia's website. Don't install off of the CD.
After you install all of the relevant drivers for your system, double check in Device Manager to make sure there are no missing drivers for anything (will have a yellow exclamation mark).
Is that all?
Are there updates or anything I need to do to the following?
1. LG optical BLu-Ray drive
2. Rosewill card reader
3. Kingwin FPX-003 fan controller?
4. HGST 4tb HDD
5. Samsung 850 pro 500gb SSD
1. Maybe a firmware update, check LG's site.
2. Possibly a newer driver, you'd have to look up your specific model/the chip it uses
3. Shouldn't be unless it has software controllabe features
5. Can install Samsung Magician. I'd suggest also going through our SSD Tweak Guide and make sure it's setup correctly: SSD Tweak Guide
You can skip the "Enable Write Caching", "Disable Superfetch / Prefetch", and disabling the Defrag/Indexer service steps. Just move the Page File to your 4TB HDD and disable it on your SSD.
And when getting all these updated drivers. Is it best to install directly from the internet onto this computer? Or is there any advantage to using my other computer and installing on a flash reader then installing on this new computer?
Yes, you can just download them all from the internet on your current system and install them. No need to use a flash drive unless you don't have internet connectivity on the new system.