What plan do I need?

In our use case, 1 user will be creating and editing all surveys, with 1 other user logging in to send surveys out, download copies and potentially run reports.

What plan do I need to be able to this? Or is it better to use 1 account, set up a never changing URL and give that to the other user to give out, set up notifications so they can download submissions, and then set aside reporting for the first user?

You didn't mentioned the volume of forms, submissions, storage etc.. that you need so basing on what you've described, you only need to have one account with one username and password to login for. You should be able to do this on a basic/starter plan.

Higher tier has a higher limit in terms of total monthly submissions, monthly payment submissions, storage, number of forms etc..

Guide: https://www.jotform.com/help/408-Understanding-Your-Account-Usage-and-Limits