Linux or UNIX based web hosting is by far the most widespread and commonly available. With most Linux based accounts you get support for CGI/Perl, PHP, MySQL database(s) and sometimes ASP support but this will be Chilisoft ASP.
This is important for you to know.
The latest version of Chilisoft ASP (version 4) is pretty impressuve since it can cope with Microsoft ASP 3.0, VBScript/JScript 5.5, and XML, but most hosts will be running an older version which means we're talking ASP 2.0 and no real effective VBScript support.
Windows hosting is usually far more expensive but offers full ASP 3.0 VBScript and JScript support by default, as well as allowing you to use the more advanced FrontPage integration into your hosted account and the possibility of using Access for small, low traffic sites or upsizing to MS SQL for large web applications.
For the vast majority of users Linux hosting is everything and more that they could either want or wish for, but anyone wanting to work extensively (or at all) with ASP and either Access or MS SQL databases should always go for Windows hosting.
I'm sorry but there is no way to answer the question without knowing the actual needs and expectations of the person who will be using it.
Some hosts allow an upward migration path, where you can upgrade from one account type to another. Some require you to buy a new account and manually move your files and folders to it once it is set up.
You've asked a very large question with no available accurate answer.
If you know what the account use has in mind then you can move from that point - otherwise, we're all in the dark.
Hope that helps a bit.