The store code is written in your address bar
You do not need to hunt for the store code a BigCommerce connection requires: it is already visible in your admin panel's address. The address has the form store-<code>.mybigcommerce.com, and the part in the middle is exactly the value you enter.
You create the access token from the store-level API accounts screen under settings. This token has one notable property: it does not expire. It stays valid until you revoke it. Not having to worry about periodic renewal is an advantage, but for the same reason the token's confidentiality matters more — if it leaks it will not lapse on its own.