You definitely don't want to use your own Apple ID - if you later part company from the organization there will be all sorts of difficulties.
The organization should create its own Apple ID and whoever is running the podcast will use that to submit it. Then the organization can give anyone who needs to access the podcast the credentials, or change the password as necessary.
You should by the way do the creation of the ID and the submission on one of their computers, not on yours (because you would need to log into iTunes with their ID and you wouldn't be able to log back into your accounr for 90 days).
Once the podcast is up and running you can maintain it from home if you want - for adding episodes only access to the feed is required and you would log into their server to access it.