I would also suggest learning 'High German' first. Even though it seems like a mythical language that no-one else speaks.
_HOWEVER_
You'll want to learn a few things in Swiss German right away:
- Numbers (so when people tell you what to pay, you sort of have an idea what they're saying, or when people tell you the time)
- The six or so verbs (reden, leuegen, schmecken, losen, laufen, and one other one, that people use here in Switzerland and are not 'High German', but that the Swiss believe are 'High German'. (I once had someone 'test' my 'High German' by asking me to 'Reden'!
) - Know that the Swiss drop of the end of the infinitive verbs
- Know that many Swiss say 'Mir' instead of 'Wir'. 'Mir leuege' means 'We look' and not a badly formed 'Me look'.