You cannot plug a Wii directly into a standard PC monitor. The signal mismatch is fundamental.
Wii analog audio (RCA L/R) → 3.5 mm adapter → monitor speakers/headphones/external speakers. Most HDMI adapters include a 3.5 mm out.
Recommendation: Wii2HDMI/KAICO for simplicity. Wii U if you want native HDMI + GamePad + Wii U games.