A PCI 3.0 card can run in a 2.0 slot without any problems. In an older game such as COD4 you will not notice any throttling with the graphics maxed out at 1080p. In some newer games you will notice it if you run at higher than 1080p on medium settings.
AMD rx580 8gb is a PCIE 3.0 and a card great card for the money if you have around a 600-650w power supply with atleast a single 4x4 (8 pin) pcie power connector. It might be OK with a 500-550w power supply depending on what CPU you are using.
A $270 1070ti is quite a bit faster than the newer $240 Amd 6500 XT, $169-$189 1650ti or $268 1660ti. The AMD RX580 is slightly faster than than the 1070 ti in some games and you can get occasionally find a new one for $140-$170.
I was getting around 189-193fps in GTA5 on High Presets and 1080p and a steady 250+fps in COD4 on max settings at 1080p with my AMD RX480 4gb card which is really really good. I bought my RX480 off of Ebay used for $80 (it was used for mining) and it lasted for 3 years but then it started artifacting really bad so I had to get another card.
Watch buying any of the cheaper $80-$130 generic brand cards from China. Since the China Crypto Ban in September 2021 there have been a BUNCH of Custom No Name "House Brand" video cards flooding the market. They are Used Mining Cards than the Chinese rebranded and added new custom coolers and V-Bios and packaging and are selling them as new. MAXSUN, ENVINDA, MLLSE, CORN, and 51Risc are a few of the brands to stay away from.
Sapphire and MSI cards with the Twin Frozr coolers are really good brands for AMD cards. They are fast and still run very cool. The Asus RX480 and RX580 cards had problems with the fans quitting after a few months. Gigabyte AMD cards were ok depending on which one, some Gigabyte cards liked to overheat in smaller cases. XFX made really good AMD cards but they tend to be a bit more expensive.
This one is cheap and you should get 250+FPS in COD4 with it no problem.
https://www.amazon.com/Sapphire-DirectX-11265-05-20T-256-Bit-CrossFireX/dp/B092NV3D1N/ref=sr_1_15?keywords=Radeon+RX+580&sr=8-15