I'm for learning High German first, but with the twist of learning a smattering of SwissGerman phrases (basically, greetings, conversation openers, excuses, thanks, conversation enders) to smooth the transition.

The reasoning behind it: German and SG grammar are pretty similar (there ARE differences), gender of the words are the same so by learning the official language you're also laying the foundation for the spoken language.
With the smattering of SG, you convey that you're making the effort (engenders goodwill) but are not there yet "so can we continue in HG bitte?".

You'll charm their pants off!

BTW, that "Hoi! Your Swiss German Survival Guide" is really good.
I can tell, I'm a native SG speaker