So without entity framework you'll be using ADO.NET (See MSDN)
Those classes you mentioned SqlConnection, SqlCommand are part of the ADO.NET framework. The two Microsoft frameworks that build on this are Entity Framework and LinqToSQL.
If you don't want to us either you have to write you own models/classes, and then methods to persist those models into your database. (This is essentially what EF does) You won't get any LINQ or designers etc.
Also, ADO.NET does have a way to create strongly typed datasets. This might help a little.
What you are doing might help you understand whats going on under the covers, but do realize frameworks like Entity-Framework save a lot of time and effort by generating models for you.