Am I Setting Up My Database Correctly? Or Am I Thinking About Things The Wrong Way?
Views: Your approach is a very widely-accepted practice. The benefits are well-documented: https://www.c-sharpcorner.com/blogs/advantages-and-disadvantages-of-views-in-sql-server1

Stored Procedures: Also, as you described it, widely-practiced (the disadvantages are notable, too) http://sqltechtips.blogspot.com/2015/11/stored-procedure-benifits.html

In my experience it's common to see views and stored procedures used for the reasons stated, and they behave as advertised. 

Whatever method you choose, I strongly advise consistency, as it can be frustrating to have to look in many places for business-rule implementation: code with embedded SQL, stored procedures, views, ORM...  try to apply some systematized implementation to limit the number of places you have to look for constraints, for example - it's possible to put them in any/all of the places I just listed.