Should I schedule the indexes in my SQL Server databases to be rebuilt before or after the statistics on my tables are updated (or does it matter)?

If you are using SQL Server and if you have the database options "Auto Create Statistics" and "Auto Update Statistics" turned on (which they should be for best overall performance), then you normally don't need to manually update statistics.

In addition, if you rebuild a table's indexes (which should be done often, such as once a week or so, depending on how heavily the database is modified) statistics are automatically updated for you, so you don't have to update statistics manually.

So if you are rebuilding your indexes regularly, you don't need to update the statistics.