I want to start running NG+ for splatoon, and I want video quality better than a potato. I know I can submit a run w/o video proof if it's a fairly low time, but I want to be prepared if my times get video-proof worthy. Also, how can I get my livesplit times onto the run video if I use a capture card?

If you're looking for cap card suggestions, I use an Avermedia LGP Lite, and it's worked pretty well for me. Some hiccups, but it's pretty much the cheapest decent option out there as far as I know. You need a computer to use it with, which leads into your other question...

Most people run their capture card into their PC and record it that way, using a program like OBS, which allows you to add other layers on top, like your splits. It's also a very handy live streaming program, so if you want to get into that... :)

Hope this helped, and good luck with your runs!