I think if you are talking about storing data Permanently or for any extended period of time you should consider Database Methods.
Thing is Application variables are open for all users on your site to see its contents. For example I used application variables to keep a track of which users were on my site on a particular time.
Session variables on the hand are created independent of any other session for each user that logs on to your site. When a user requests your site from the server, the server creates a session specifically for that user. Each session has a timeout and it gets destroys after the timeout has elasped. This is generally used to store SMALL amounts of data and it is global in the sense that the variable can be accessed from whatever the user is on given the timeout has not elasped.
The other methods I don't like or are not familiar with. Server.execute just pauses processes of one page.... processess another in the parentheses and then resumes processing of the main page. Don't see how that is even relevant. Cookies you could maybe do some reading on but I don't know too much to comment about that but my suggestion is this:
If you are thinking of storing data, and if you are thinking of going larger scale at any point in time in terms of your site. You're gonna need physical storage, because you cannot rely on any of the variables i mentioned earlier to store any large amounts of data. Possibly cookies might be a interesting solution and you could do some reading but I SUGGEST DATABASE!!!!