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Your first option should enable you to transit without a visa, thanks to your US visa. Otherwise, Indian citizens do need an airport transit visa in Germany.
Your second option is covered in earlier questions, in particular Is a Schengen visa/transit visa required for a transit flight through two Schengen airports? You would need a type C Schengen visa (and not an βairport transit visaβ) as you would enter the Schengen area in Zurich and take a flight between Schengen countries.
All the rules are detailed in Do I need a visa to transit (or layover) in the Schengen area?