I'm completely noob so apologies if this is dumb but I was curious what is the optimal way people who speed run DS games do this. Do you play through an emulator or on the handheld? If on handheld, what method should i use to record gameplay for runs? If on an emulator, what emulator do you recommend?

For emu, idk. For console, well, it depends: you can go with a 3DS or a DS capture board (3DS is still quite expensive though); http://www.3dscapture.com/ & http://www.3dscapture.com/ds/index.html

Still, for 3DS, i heard of another solution that's basically streaming through wifi to your computer. No idea how that works though.

What I do personally since my DS has homebrew is I can record wirelessly through a program, although you'd need a new3DS for that, there's an emulator though for PC called desmume, I'm not too sure how well it runs all the games but it does work, for handheld depending on the length of the games you could always set up your phone or whatever you have to be a set distance from your DS and record like that, otherwise you'd need a capture card for the DS

I'm not sure about emulator, but I use the actual handheld. I had a capture card installed, and it runs through it's own software that comes along with it. I then capture both windows in OBS/Xsplit . The capture card itself is a little expensive though.