Permission:
- Contact: Global, Read = Yes (to view), Append = Yes
- Lead (probably): the scope will depend on what you are doing: Create = Yes, Edit = Yes, Append To = Yes
For simplicity, often when creating/editing is allowed both Append/Append To are set to Yes.
And the Permissions assigned to an appropriate Web Role that is attached to the portal user's contact record or one of the default Web Roles for authenticated users etc that the portal user inherits from.
Depending on what you are doing please be mindful that Global read can potentially present Privacy issues where it is assigned to external users.
Note: if you are not seeing the full list make sure you have cleared the portal cache (<portalurl>/_services/about when logged into the portal with Adminstrators Web Role assigned or there is a sync button in portal editor) and have logged the portal user out and back in.
