Anything you can capture, OBS needs to render before it can encode. You're nearly always best served by giving OBS the best GPU you can justify. If you're trying to capture 4K, that just makes it more crucial.
A capture card doesn't do the work of a GPU, and it doesn't do the work of an encoder (generally). It's to allow for separation between the job of generating the frames you're capturing, and then capturing/rendering/encoding those frames by using two separate machines. Depending on what you're capturing, though, that could mean you need TWO good GPUs instead of one.
A capture card is generally meaningless in a single PC setup, unless you're capturing from another source like a console.
Generally speaking an NVidia card with the NVENC encoder, the newest you can justify, is going to reduce load on your gear more than an otherwise comparable AMD card, because it will remove load from the CPU for encoding without placing it on the GPU (because it uses dedicated hardware for the compression).
The R 290 is, at this point, a six year old GPU. I imagine OBS would struggle to render 4K60 on it.
I believe the 1660Ti is currently the cheapest available Nvidia card with the newest possible hardware encoder on it.
