Will my SQL query use stale data? How can I prevent it?

If you're using the default isolation level in SQL Server (Read Committed), then you certainly can run into all sorts of issues around inconsistent reads. Paul White describes the problems here.

If you want your read queries to read data which is fully consistent to how it looked at a given point in time, I'd recommend that you consider Read Committed Snapshot Isolation (RCSI). With RCSI, your query will return data that is consistent to a single point in time (the start of your query). If User A starts a SELECT query while User B is concurrently performing updates, User A will read the "old" value because it will read a snapshot of the data, which is consistent to the start of the query.

The catch with RCSI is that it's a database-level setting. Unlike Read Uncommitted, you can't set it as a session-scoped setting. You'll have to consider this change more globally before making the change. However generally speaking, if you require consistent reads for this query, you probably want consistent reads for the entire application.

While the Repeatable Read isolation level may look appealing to solve your problem, but note this detail from the linked post:

The repeatable read isolation level provides a guarantee that data will not change for the life of the transaction once it has been read for the first time.

This means that the data can still be changed prior to being accessed, but during the time your query is running. It is also subject to some of the same inconsistent reads as the Read Committed isolation level--notably phantoms.