For Frigate you can just add a Coral TPU to offload the heavy lifting but with Jellyfin you'll likely need a GPU/iGPU (Intel) that can handle transcoding. I don't know what specific models you're looking at but you might try to determine their passmark score. I think it's recommended at least 2000 score for a single 1080p transcode. Alternatively you can stick to specific file formats that won't need transcoding but this might be some work.
You could get a used Dell Optiplex micro. They have i3/i5 processors and can be found for around $100. This will at least get you going and you can always build something later.