You need to put the CTE first and then combine the INSERT INTO with your select statement. Also, the "AS" keyword following the CTE's name is not optional:
WITH tab AS (
bla bla
)
INSERT INTO dbo.prf_BatchItemAdditionalAPartyNos (
BatchID,
AccountNo,
APartyNo,
SourceRowID
)
SELECT * FROM tab
Please note that the code assumes that the CTE will return exactly four fields and that those fields are matching in order and type with those specified in the INSERT statement.
If that is not the case, just replace the "SELECT *" with a specific select of the fields that you require.
As for your question on using a function, I would say "it depends". If you are putting the data in a table just because of performance reasons, and the speed is acceptable when using it through a function, then I'd consider function to be an option.
On the other hand, if you need to use the result of the CTE in several different queries, and speed is already an issue, I'd go for a table (either regular, or temp).
WITH common_table_expression (Transact-SQL)