This is not the worst moment for a small upgrade like this. I sometimes browse deals just out of boredom.
GPU: AMD Radeon R7 360 Series (18385 MB total memory)
That VRAM statement has me very confused.
First of all, are you absolutely sure it doesn't run on your current system, here is the thing, if you are going to play the game anyway, and you are willing to upgrade too. Well you might as well just buy the game and check and see, you know? But sure it would be a pretty degraded experience presumably looking by the recommended specs.
The thing with the pcie generations is very true, something to keep an eye out on when it comes to low end cards release since 2022'ish.
If I were you I would try to stick to something with very comporable power draw to your old GPU, your power supply is old, and allthough this is just anecdotal evidence, I've seen two old systems die (mainboard went out in both cases) some time after upgrading gpu+psu, and these are like the only desktop computers I've ever seen die under my supervision.
I'm going to go with european prices (mostly german prices)... If you're in the states you should be able to find even better deals, I think. I shall avoid intel gpu's for the reason that, going by your current specs, I presume you play a fair amount of older direct x9 titles, and intel deals with these through a "translation layer", the support for these games is less optimal when compared to nvidia and amd. One further note... Since you are on skylake (the last intel CPU generation to support windows7) you might be running/want to dualboot w7; in that case your support ends at the nvidia rtx2000 series and the amd rx5000 series.
Ok what can you actually buy new. Weird thing some lower end cards reappeared on the market that weren't exactly available during the corona/mining craze price hikes.
Rx560 --- 75watt
Rx570 --- 150watt
They do not constitute a big upgrade for your, but they are probably the cheapest (unused) cards you will be able to find, and they do fall within minimum specs, but don't quite make it to recommended.
https://www.idealo.de/preisvergleich/OffersOfProduct/6854717_-radeon-rx-5700-challenger-d-oc-8gb-gddr6-asrock.htmlI don't know why this rx5700 was nowhere to be found two years ago, but this is a pretty ok deal. It does draw up to 180 watts though. Given who is selling it (3 aggregators in the style of amazon) I would not expect this offer to stay up super long. Also technically it's pcie 4.0 - but contrary to say a rx6400 it has the 16 lanes (x16), so it is much less of an issue.
On nvidia side:
gtx1650 -- 75watt these go around the price of that rx5700 offer tho you can find slightly cheaper, they don't pack the same oomph, but it's a neat card
gtx1660 -- 120watt still well below your stated budget, a little hard to justify given the deal above since it's a little slower
rtx2060 -- 160watt probably your cheapest buy-in into raytracing, dlss, superressolution and a bunch of other stuff that is cool, but that I wouldn't get to hung up about
rtx3050 -- 130watt honestly if you can find it below 300€, it's fine... fastest of the bunch, your problem is, that it's pcie 4.0 x8, that is really suboptimal
Same problem presumably goes for the whole rx6000 and rx7000 lineup, over at amd... Check in detail and you might be able to find something that is pcie4.0
x16 and below 300 bucks, but I'm pretty sure you are looking for special offers at that point.
ti and XT, and super variations of these models might differ vastly or barely at all, allways look at how many watts they draw, that + what year it came out, gives you a good idea of what "tier" of gpu we are talking about.
Yeah the whole pcie4 thing really puts a nasty stick into your wheels, but if you are not happy with those choices and concessions, there still is the used market, rx5600, gtx 1060,1070,1080, and rtx2070 might all be worth looking into. To reassure you tho: I'm running a 2080ti which outclasses all these cards on pcie3.0 and it's fine. See they're cutting costs because pcie4.0 x8 is the same bandwith as pcie3 x16, but if you constrain pcie3 at x8, you are at half the bandwith. In real life that does translate to perfomance losses tho tbf, even then most stuff remains still perfectly playable.
Hope that was more helpful than confusing, lol.
https://www.idealo.de/preisvergleich/OffersOfProduct/7020630_-radeon-rx-5600-xt-phantom-gaming-d2-6g-oc-asrock.htmlappeared, it's 30 bucks less than the 5700