Can anyone recommend a way to get a "County" field on a customer record?

create a custom entity list field where the source list is country

Sorry, I was referring to US Counties not Country.

you may be doomed to create your own list of counties

NetSuite doesn't have a built-in County field on Addresses, as only a handful of countries have such territories, so you could either add a new custom field to Addresses or a new Entity field.

So I have already created a customer record with the Primary key and name being the zip code(county data was easy to obtain and will upload in just a few hours). I am having trouble finding any way to get NS to associate the customer's {billzip} with the custom record's zip code so that I can then source list the county into another custom entity field.

Our company recently found out that there are zip codes that straddle 2 or more counties, so this is not always going to work. Short of having an address verification or geolocation service, some zip codes will match multiple counties.

I am really not concerned about that, I have solid data mapping zip codes to counties that we used in our legacy system for years. I am just having trouble doing a join from the {billzip} on the customer to the zip code on my custom record.

Alright. Well, since billzip is not a List/Record field, it has no join fields available to it. You can't really join it to other record types using standard functionality. You would need to write a script to search your custom record type, looking for the record with zip code matching billzip, then set your custom county field accordingly.