Which Swiss language to learn first

Switzerland has four official languages. You do not need to speak all of them. You need to speak the one where you actually live, well enough to be polite.

In Zurich, Bern, Basel, Lucerne, Sankt Gallen, Zug: learn German. Standard German (Hochdeutsch) is fine to start. Every Swiss German speaker understands it. Swiss German (Schwiizerdütsch) is spoken, rarely written.

In Geneva, Lausanne, Fribourg, Neuchâtel, Valais: French. Standard French, no dialect surprise.

In Ticino: Italian. In Graubünden: mostly German, with pockets of Romansh and Italian.

For settling in, aim for A2 in the first year. Migros Klubschule and Ecole-Club are cheap and everywhere.