[SalesForce] assign Permission set to a profile instead of user

This works:

• Create permission set P1 with record type R1 only assigned to it
• Create permission set P2 with record type R2 only assigned to it
• Add P1 or P2 to the appropriate Users
• Ensure R1 and R2 are not set on the profile, leaving just the Master record type selected there

Then when the SObject is created it is automatically given the record type according to the permission set of the user (with no record type selection prompt) which is the behaviour I believe you want.

You're missing "full" control of the record.

The levels of control are, in ascending order:

• None
• Read
• Edit
• Transfer
• Full

Each level of control implies the additional permissions that are lower than that, unless prohibited by the profile.

Full control can generally only be granted by:

1. owning the record
2. being a manager of the owner of the record (if enabled), or
3. having Modify All Data for that object (included automatically if you have the global Modify All Data permission).

See the Help & Training modules on Sharing for more details, as well as other answers here on the SFSE.

"Full" control is also referred to as "Owner" permissions when viewed in Sharing, but basically just means "Delete", as that is the only additional permission it grants. You can have Transfer independently of Delete on some objects by Sharing Rules or Organization Wide Defaults, and you're also explicitly granted Transfer when a record is owned by a queue you are a member of or is in the same Territory as you with Territory Management and the appropriate settings.

As an exception to granting Full access, the "Financial Edition" of salesforce.com, used by companies like Merrill Lynch, offers the ability to create sharing rules that grant Full access to a record despite not meeting the usual criteria.