If your app is .NET, look at Sustainsys (https://saml2.sustainsys.com/en/2.0/) or ITFoxtec (https://www.itfoxtec.com/IdentitySaml2) libs. Unfortunately there isn't a clear architect/dev-level guidance at the protocol level on key decisions that need to be made when implementing SP that tightly integrates with your app. Give one of these a shot and post your questions on StackOverflow.