Id like to ask users for their country of residence on signing up and then separate them into different lists on Vertical Response...is this possible?
Unless some talented coder with aMember expertise is willing to provide custom written code for free, I suspect your best option is to request a quote for the job from aMember.
As far as I know, none of the aMember commercial email list server integrations is going to support this. I don't know how many users you are anticipating; however, you should be able to handle this manually. You could use a custom field to gather the user's country during aMember signup. Use a mail list integration that would automatically add new users to a mailing list (and supports the addition of a custom field ("Country"). Manually edit the users account in the mail server to include the country.