Hi there,
you don't say if you're using Unix/Windows, but the installation on either shouldn't be too difficult as you can download the 'installer' versions for each app on Windows and it pretty much takes care of everything (just tell it where you want the apps installed, usually C:\ is fine), while on RH, it should be a case of reading through the README files as they give you both the quick and in detail versions for installing each app.
Basically, it will take the same effort to install the required apps on your laptop as it did installing it on your work's server, so there isn't an easy way round I'm afraid, as you are needing the server to serve the pages, PHP to parse your .php files, MySQL to administer and handle your database stuff and perhaps PHPMyAdmin for a web based MySQL administration interface.
Once you have downloaded and ran the installers, the README's for each app will guide you through configuration for your chosen platform and get you up and running in no time