If you’re using NetworkManager, I’d recommend you to use it to create a VPN profile instead and connect to that on startup through the unprivileged nmcli.
The 710M will give you trouble. Like, pain in the ass. See if you can disable it in BIOS; you won’t be using it for “serious” gaming anyways.
Distro doesn’t much matter. It’s fully up to personal preferences. Try them all (using Ventoy like @b9chomps recommended. Some distros make the installation and management of the Nvidia driver easier than others but you should ideally be disabling that GPU entirely.
I personally recommend Fedora to newcomers but as I said, that’s personal preference.
Note that if some piece of hardware (i.e. wifi) doesn’t work in one of them, it most likely won’t work in any distro.
It has the option of UEFI but the GeForce (I think) doesn’t support it.
This doesn’t make much sense to me. The GPU plays no role in that part of the boot process.
I’m planning to upgrade the RAM to 8 gigs and upgrade to an SSD
Get an SSD now. Even a dirt cheap one. 4GB is tenable with careful management but a hard drive will make everything excruciatingly slow, even on Linux.
Distros that don’t respect your privacy are hard to find, so privacy isn’t really a factor here. You’re just going to get everyone’s favourite distro here, regardless of whether it fits your other requirements.
What kind of hardware do you use?
How stable or fresh would you like your distro to be?
What wind of desktop experience do you prefer?
Also note that the apps you use (on your PC or in the browser) usually far outshadow the OS w.r.t. privacy intrusion.