I’m using your third option and it works great.
My stored procedure has a table-valued parameter. See also Use Table-Valued Parameters.
In the procedure there is one statement, no loops, like you said:
UPDATE table1 SET somecolumn = 'someVal' WHERE ID IN (SELECT ID FROM @definedTable);
It is better to call the procedure once, than 1,500 times. It is better to have one transaction, than 1,500 transactions.
If the number of rows in the @definedTable goes above, say, 10K, I’d consider splitting it in batches of 10K.
Your first variant is OK for few values in the IN clause, but when you get to really high numbers (60K+) you can see something like this, as shown in this answer:
Msg 8623, Level 16, State 1, Line 1 The query processor ran out of
internal resources and could not produce a query plan. This is a rare
event and only expected for extremely complex queries or queries that
reference a very large number of tables or partitions. Please simplify
the query. If you believe you have received this message in error,
contact Customer Support Services for more information.