Capture Card Notes

Analog option 1:
S-Video cable
Use for: NES/SNES/N64/GC
capture:
External - GV-USB2 or similar
Internal - Avermedia C027
You can also use a composite cable (yellow/white/red) with these but s video is around the same cost and looks much cleaner.  Most NESes and systems in the PAL region only have the composite option.

Analog option 2:
Component cable
Use for: Wii
capture:
External - Startech USB2HDCAP/USB3HDCAP
Internal - 	Avermedia C027
			Datapath Vision E1/E1s (for pixel enthusiasts, doesn't capture sound)

HDMI:
Use for: GC with Adapter*(3)/Wii U/Switch/*(4)
capture:
External
	Avermedia LGP Lite, Live Gamer Mini
	Elgato HD60 S
	Magewell (supports linux)
Internal
	Avermedia c027, Live Gamer HD 2, Live Gamer 4k
	Elgato HD60 Pro, 4K60 Pro mk2
	Datapath Vision E1/E1s (for pixel enthusiasts, doesn't capture sound)

DS/3DS USERS
An internal modification to the system is needed to output video.  You can purchase these mods from merki.  This is an allowed mod for speedrunning, other methods like CFW to stream capture over WIFI are treated as a separate category.
https://www.merki.net/
NOTE: Original DS is currently out of stock and is likely to remain that way for a few months

TIPS
1: don't play by watching OBS!  use a powered analog splitter for composite/s video to a separate monitor.  For HDMI you can use a powered splitter or pass through your capture card if it has an output.

2: internal capture is better than external, which is why it's more expensive.  If you have any idea how to add a card to your desktop that will work better than USB based capture.  Check to make sure you have enough slots on your motherboard and open lanes.  If you do go with USB, USB 3.0 based cards generally work better than USB 2.0.

3: The original GameCube model DOL-001 is capable of native HDMI output with an adapter.  The Insurrection Industries Carby and Eon GCHD Mk II on the 3.0 firmware (can be sent in to update if needed) provide the best picture possible.

4: Analog outputs can be converted zero-lag to HDMI with the OSSC or RetroTink 2X.  The RetroTink is better for 240p sources (NES/SNES/N64) and the OSSC for 480i/480p (GC/Wii).  This can be expensive, but it allows you to use an HDMI capture card and split to an HDMI TV/Monitor without introducing input lag (apart from any lag inherent to your monitors).