If you want to permanently number the rows in the table, Please don't use the RID solution for SQL Server. It will perform worse than Access on an old 386. For SQL Server simply create an IDENTITY column, and use that column as a clustered primary key. This will place a permanent, fast Integer B-Tree on the table, and more importantly every non-clustered index will use it to locate rows. If you try to develop in SQL Server as if it's Oracle you'll create a poorly performing database. You need to optimize for the engine, not pretend it's a different engine.
also, please don't use the NewID() to populate the Primary Key with GUIDs, you'll kill insert performance. If you must use GUIDs use NewSequentialID() as the column default. But INT will still be faster.
If on the other hand, you simply want to number the rows that result from a query, use the RowNumber Over() function as one of the query columns.