How to setup SQL Express for course use

I will be teaching a web scripting course, and I would like to switch from using MS Access to MS SQL as a database. Please forgive my ignorance, as have much to learn about SQL Express. We have installed SQL Express on a web server (windows box).

Question1:
is SQL like MS Access, in that the SQL Express software should be installed locally on the users machine. The user will create databases and tables locally, then upload the resulting database(s) to the appropriate folder on the web server along with web scripting files?
-- OR
is MS SQL like MySQL, where the db is installed on the remote server, and user accounts are created within the database with appropriate priv.'s. The user logs in to the db application remotely to create tables within a given database.

You can install it either way (locally or remotely). I could see advantages to both. If they install it locally to each machine, you wouldn't have to worry about setting up users/permissions/remote connections, etc on a central server. But if you install it on a central server, you only have to go through the install one time and don't have to worry about the student upload/transfer.

If you don't have much experience with Express, I'd suggest installing Express Advanced so you can get the GUI management tools as well.

Thanks,
Sam Lester (MSFT)