Lithium is correct is what he has stated.
Do you already have an SQL server running at your school?? if you do can you not create a new database on there??
If you do decide to go the MS SQL Express route I would also use mixed mode authentication as Windows only authentication can be difficult to setup.
This link cover step by step installing of MS SQL Express:
How to: Install SQL Server Express
This link covers step by step installing of MySQL:
MySQL :: MySQL 5.0 Reference Manual :: 2.4.8 Installing MySQL on Windows
To install MyLittleHelpdesk follow these steps:
1 - Create an empty MySQL or MSSQL database with the relevant user access.
2 - Unzip and upload the MLH folder to the root of your website.
3 - Edit the details found in the incs\db_connect.asp file with the details of you databse server and user.
4 - Point your browser at http://{your_url}/MLH/Install/ and follow the install wizard.
5 - Your helpdesk is now ready to use.
Let me know if you need anything else