Medium Trust is not required, it is something enforced by security policy at many shared hosting environments, it is supported but it poses some issues with skins and also NeatUpload does not work in medium trust so you don't get the progress bar when uploading.
In .NET 4, there are less problems with skins under medium trust but still the problem with NeatUpload.
I recommend use .NET 4 rather than 3.5 if possible.
The /App_Data and /Data folders must be writable by the web process user (the identity of the application pool)
Hope it helps,