What might I need to change about this/upgrade later if I were to upgrade to a 144hz monitor, if anything? I'm perfectly fine with not being able to run everything in absolute full blast mode at max possible FPS, just... "good" is sufficient.
Running every game at 144Hz, even at 1080p, is basically impossible. You can throw a 4090 in there and it still won't work; the CPU matters as well, and many/most games just aren't well enough optimised to hit that target. Some are small enough that it isn't an issue, but anything that even tastes of high-end graphics won't manage.
On the other hand, an 144Hz desktop is a completely different feel from a 60Hz one even if the games can't manage it.
Once you start thinking of higher-end monitors, the way to go is actually Freesync and/or G-Sync Ultimate*. That lets the monitor present frames at whatever rate your computer actually outputs, and almost entirely eliminates stuttering. This is especially important because, uh...
Imagine you have a monitor that's set to 144Hz. If the game is capable of rendering at 120Hz, assuming you don't turn v-sync off, you will not be getting 120 frames per second on the monitor. It'll actually be limited to 144/2, 72Hz. And if it can't hit 72FPS reliably, then... yeah. Free/Gsync entirely eliminates that.
But it does cost quite a bit more. While the modules themselves aren't super expensive, you'll only find them in mid to high-end monitors.
*: But not the older versions of g-sync, because those modules have a constantly running fan on them... it got annoying in a hurry. Yes, that's 'constantly' as 'even during standby', in the case of mine. Augh.
= = =
One final concern. If you have any thoughts of running Stable Diffusion, you
need an nvidia GPU.
Oh, and on the subject GPUs. While a low-end GPU can certainly drive 1080p — it requires somewhere between 1/2 and 1/4 the GPU horsepower of 4k — this is only true if the GPU still has enough VRAM to load the game assets in. Games scale to available VRAM, but only so far, and the moment it doesn't all fit in at once, your performance will drop off a cliff.
GPUs can swap textures out to main memory, but that's pretty much like main memory swapping to disk. In severe cases, your framerates can easily drop by 90%.
GPU memory has been rapidly increasing over the last couple of years, so while 3 GB was okay a few years ago, today it's woefully inadequate. 6GB will work in most cases... today. But I honestly wouldn't buy a GPU today with less than 12.
Fortunately there's a 12GB RTX 3060 model, so you have options.
