Xbox 360 AV cables (Composite/Component) are legacy accessories—available used/refurbished.
HDMI Mod (Xbox 360)—Xbox 360 HDMI Adapter (Keboard/Chimeric) or internal Xbox 360 HDMI Board (RetroGEM, Kaico)—Digital 1080p, no upscaler lag. $50–100 installed.
AV cable works. HDMI mod transforms the experience.