Wyoming web based LLC
1. Publish an Oregon phone number & PO Box on the web site for orders & customer service,
2. Ship product from Oregon?
3. Deposit payments to an Oregon bank?
Typically with a business that is conducted solely online, you would be able to register your business in any state, such as Wyoming, and use a PO Box and phone number in a different state on your website. However, there are a few limitations to consider:
When you say the products would be shipped from Oregon, this would technically create a "nexus" in the state of Oregon, meaning you would need to collect sales tax in Oregon (and to do that you would need to obtain a sales tax ID). If you have a warehouse or an office where you are storing or exchanging the products to be shipped, or have any employees in Oregon, then you would be required to registering in that state (either as domestic or foreign entity).
If the company is registered using a home address in Oregon and you have no employees, then you could in principle register that business in Wyoming, until it grows bigger to require Oregon registration.
Regardless what state your business is registered in, you generally don't have problems using a bank in a different state.