Filtering Best Practices

What are the best practices for filtering out a big list?

1. Keep all filters wide open all the time

OR

2. Narrow filter values down as I add a Filters somewhere else?

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For example let's say I have a List with thousands of Students.

The Columns I can Filter on are: First Name, Middle Name, Last Name

I have 100 students with the last name Anderson and 100 students with the last name Smith.

Now I go to my Last Name column and Filter by both Anderson and Smith. When I go to the First Name column to add an additional filter, should I see the thousands of First Names OR should I just see the 200 First Names that belong to Anderson and Smith?