Angels have the Phone Box
First, let me point you in the direction of our nVidia thread, which has the most current drivers link in the first post, and is constantly updated as necessary. There is a lot of good historical information in that thread, so you might want to have a read through it as well.
Latest NVIDIA GeForce Graphics Drivers for Windows 10 - Windows 10 Forums
For upgrading your system, It's recommended that you disconnect all peripherals, uninstall any 3rd-party AV software, remove monitoring software (i.e. Speccy), and run sfc /scannow to make sure all system files are intact. You can also check drivers in Device Manager, right-clicking each one and having Windows auto-check for updates. If sfc /scannow says it's unable to fix corruptions, reboot and run again. Sometimes it can take 3 runs with reboots in-between before thing gets fixed. We're looking for "no integrity violations found" result.
If driver updates do not put the most recent nVidia driver in your W7 system, download the current one to your desktop and have it ready for your W10 upgrade.
Make sure you have a good image of your W7 OS, then download the ISO from MSTechBench, extract to desktop, and run setup.exe to upgrade the system.
You are correct, that the system should be run for a little while after the upgrade, as things are running/updating/indexing in the background after the update.
Once the upgrade is completed, turn off Fast Startup.
Turn System Restore on. Set a restore point.
Once the activity on the C drive has calmed down, do a shutdown/startup (not reboot) or two.
If the nVidia card is working and everything seems fine, connect your external monitor.
If you have video issues, install the latest driver. Make sure everything is working, then connect your external monitor.
Check if Windows is activated. It probably will be, since you've upgraded already. If not, use your W7 key to activate the OS.
Good luck and let us know how it goes.