Is using the singleton pattern a good idea when accessing libraries using MVC?

I have a web app, this app as you already know will have a lot of requests, and each request will run on a different thread, meaning that if I use singleton to access my DAL library it will not be a problem.

However I'm unsure about wether this is the best approach, because I read that one request my use different threads sometimes, and I have also read that locking threads may cause a performance lost sometimes when using single instances.

Just so you understand me better this is what I plan to do:

DAL <- SingleInstance <- BAL <- SingleInstance <- Controllers <- Views

Is this a good approach?

This is the singleton I plan to use:

     public static Products Instance
        {
            get
            {
                return Nested.instance;
            }
        }

        class Nested
        {
            // Explicit static constructor to tell C# compiler
            // not to mark type as beforefieldinit
            static Nested()
            {
            }

       internal static readonly Products instance = new Products();

Note: My Dal will access the database using ADO.NET(I have my reasons to use ado), and the BAL will only use this method to do select or CRUD operations. Thanks.