Get the laptop with the best, newest Nvidia GTX level card you can justify. You want support for the latest version of the NVENC encoder you can get.
AMD may get you more performance per $ but there are sometimes compatibility issues that take time to work out. YMMV.
Not sure what you mean by the external recorder-- if it's a standalone recorder its own encoder and HDMI input, then it doesn't matter what CPU or GPU your computer has; OBS would only be handling the streaming encoding and the recorder would just take the video from OBS.
Without information on what kind of content you're dealing with its hard to advise on what is necessary.