My thinking is that if I put my ANDs that filter out a greater number of rows before those that filter out just a few, my query should run quicker since that selection set is much smaller between And statements.
But does the order of AND in the WHERE clause of an SQL Statement really effect the performance of the SQL that much or are the engines optimized already for this?
Depends on the server.
PostgreSQL, for example, will optimize the query for you.
It really depends on the optimiser.
It shouldn't matter because it's the optimiser's job to figure out the optimal way to run your query regardless of how you describe it.
In practice, no optimiser is perfect so you might find that re-ordering the clauses does make a difference to particular queries. The only way to know for sure is to test it yourself with your own schema, data etc.
Most SQL engines are optimized to do this work for you. However, I have found situations in which trying to carve down the largest table first can make a big difference - it doesn't hurt !
A lot depends how the indices are set up. If an index exists which combines the two keys, the optimizer should be able to answer the query with a single index search. Otherwise if independent indices exist for both keys, the optimizer may get a list of the records satisfying each key and merge the lists. If an index exists for one condition but not the other, the optimizer should filter using the indexed list first. In any of those scenarios, it shouldn't matter what order the conditions are listed.
If none of the conditions apply, the order the conditions are specified may affect the order of evaluation, but since the database is going to have to fetch every single record to satisfy the query, the time spent fetching will likely dwarf the time spent evaluating the conditions.