In my experience editing 4K, VRAM is your biggest bottleneck. If you want the best bang for your buck under 500 dollars, look at the Sapphire Pulse Radeon RX 7800 XT 16GB. That 16GB buffer is crucial when you start adding color grades or noise reduction. Ngl, Nvidia has better codec support, but at this price, AMD gives you way more raw horsepower for the money.

For 4K under $500, you might want to consider the ASUS Dual GeForce RTX 4060 Ti 16GB. Make sure to get the 16GB version, 8GB just wont cut it for DaVinci Resolve.

To give you a decent recommendation, we kinda need a bit more info first. What editing software are you planning to use? Premiere Pro and DaVinci Resolve handle hardware pretty differently, so that makes a huge difference in what card you should get. Also, what does the rest of your PC look like? If you are running an older CPU or only have 16GB of RAM, dropping 500 bucks on a GPU wont magically make 4K editing smooth anyway. You need a balanced system for this stuff, otherwise the new card is just gonna sit idle waiting on your processor. Let us know the specs and software and we can go from there...