SQL UPDATE WHERE IN (List) or UPDATE each individually?

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.

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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.

Your first or third options are the best way to go. For either of them, you want an index on table1(id).

In general, it is better to run one query rather than multiple queries because the overhead of passing data in and out of the database adds up. In addition, each update starts a transactions and commits it -- more overhead. That said, this will probably not be important unless you are updating thousands of records. The overhead is measured in hundreds of microseconds or milliseconds, on a typical system.