You are smart to be thinking of designing a Data Layer in your app. In an ASP.NET application this will help you standardize and pretty dramatically simplify your data access. You will need to learn how to create and use ObjectDataSources but this is quite straightforward.
The other advantage of a data access layer (built using a separate project/DLL) is that it makes Unit testing much simpler. I'd also encourage you to build a Business Layer to do much of the processing of data (the business layer, for example, would be responsible for pulling ObjectDataSources from the DAL to hand to the UI code). Not only does this let you encapsulate your business logic, it improves the testability of the code as well.
You do not want to be caching DataSets (or DAL objects, for that matter) in the session! You will build a Web app so that record modifications work through a Unique ID (or other primary key spec) and feed changes directly to the DAL as they are made. If you were to cache everything you would dramatically reduce the scalability of your app.
Update: Others on this thread are promoting the idea of using ORMs. I would be careful about adopting a full-blown ORM for reasons that I have previously outlined here and here. I do agree, though, that it would be wise to avoid DataSets. In my own work, I make extensive use of DataReaders to fill my ObjectDataSources (which is trivial due to the design of my DAL) and find it to be very efficient.