I live in Switzerland and my shopify store is configured as such.
The problem I have is there are some limitations. For example:
I don't live in US, but can I change my shopify business to be configured as US.
Thanks for your help!
Since you're operating out of Switzerland it would be better for invoicing, Taxation and the like to keep the Switzerland address.
To use Shopify Payments you would need to provide proof that you are in a supported country, so won't make much of a difference anyway.
To overcome the currency issue you can use Shopify Plus to configure it natively but that might be too costly if you're just starting out.
Let me know if you have any questions, happy to answer them.