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@beehaw.org 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.

KDE Plasma (love the looks of it, though is my hardware enough?)

With 8 GB RAM and SSD, it should be plenty. Otherwise, I’d go with something else. XFCE is quite a solid experience, as I recall. No strong recommendations there, though. I’ve mostly used Cinnamon and KDE over the years.

Linux Mint is a classic choice. Positive: It has been recommended to newbies so much over so many years that there are tons of entry-level how-tos. Downside: Many of them are old and might be outdated by now. Be sure to always check whether the guide you are following is from 2010 or something…

Same really for all the Ubuntu distros. Kubuntu (=KDE+Ubuntu) worked fine for me.

I’ve read many people being very satisfied with Pop!_OS as well. Apparently, it’s a good distribution if you want everything to already be set up for gaming for you. Haven’t used it myself, though.

EndeavourOS is the one I’m personally planning to use whenever I next install an OS. The distro and the surrounding community have a great reputation for being user-friendly and reliable.

For such an old system, your DE matters more than anything. I'd recommend XFCE, or even LXQT. Definitely upgrade your RAM though, that'll give it a nice boost - DDR3 should be pretty cheap now. Any cheap SSD should be a big improvement as well.

I've got Zorin installed on my mum's PC (which is just as old as yours), and it works really well, even on a regular HDD.

i don't think my preferences line up with what you're after, so maybe ignore this. . . .
i'd recommend explaining computers youtube and website for beginners - he'll give you much better advice than me
https://yewtu.be/channel/UCbiGcwDWZjz05njNPrJU7jA

but FWIW i reckon mint+xfce. will give you "easy" and "decent performance on old hardware"

you can try out the more flashy d.e s on a usb boot drive see if you think the features are worth it on your setup.

always remember it's easy and cheap to experiment.

get yourself a system for backing up your "home" directory, - a couple usb drives is easy enough.

and i'd also recommend starting a text file list of all programs/packages you like to install.
you can make it into a bash "sudo apt get " script (for debian based) if you're feeling super lazy.
, or just run through it manually whenever you switch.

also do the SSD upgrade as soon as you can afford it, it'll make everything a lot better

Have fun.

I recommend installing Ventoy onto an USB thumbdrive and booting into some of your candidates. Since it boots from USB the performance isn't 100% representative, but you can check if you get any driver issues and how the DEs "feel".

P.S. Eternity for Lemmy is making its first steps and was forked from Infinity for Reddit (I believe)

On the old NVIDIA driver, if you're brave, they're still available and on Arch(-based) pretty easy to install. I used some old desktop GeForce 6xx with it last time around 2020 and it worked for basic stuff, like desktop compositing, OpenGL games or even some WineD3D. Don't expect it to run anything somehow modern. And yes, with the driver you're limited to X11 session.

If you also have iGPU and it's switchable, the only option to somehow achieve offloading (switching the graphics dynamically) would be through unofficial methods like Bumblebee.

Also, graphics that old should have some support in the open source Nouveau driver, that will probably be loaded by default on most distros. If I'd be stuck with such chip, that would be my first thing to check if it isn't enough for my planned use-cases.

Your distro preferences don't line up with your DE preferences at all. While you CAN install any DE on any distro, doing so often negates the point of using said distro in the first place.

Some KDE suggestions would be KDE Neon and Kubuntu, neither if which I've ever used, or openSUSE which I highly recommended.

I think that EndeavourOS with XFCE would be lightweight enough, but I'm not sure if it's as reliable as Mint, I have used it for few days only.

KDE in 8GB RAM won't leave you much room for applications. If you can't get more memory, I suggest trying a lighter desktop environment, or maybe using ZRAM or ZSWAP.