You could use the belkin router that I referenced in an earlier post and that will get you a small private wifi/network connection between your iPad and iPhone regardless of what security the school has in place. If you get an Apple TV device for $100, you can lose the VGA dongle as this will also connect to the iPad via wifi. You definately will want to password protect both access to the router setup and to its wifi connection (use WPA).
To get internet, you will need the cooperation of the school so that you can connect the internet port on the router to the schools network. I would first try connecting the router to the data jack in the classroom. Most networks are secure for wifi, but not always for hardwire connections - at least not to access the internet. If you do this, make sure that you use the "internet" jack (sometimes called "WAN") on the router so that your little private network is isolated from the school's network.
The above setup won't allow you to access the school's network resources like shared drives, but should allow you to use an iPad and iPhone for your presentations, along with access to the internet.
Note: School or corporate policy might prohibit you from connecting any kind of wireless or network device on their premises. Don't get yourself in trouble, check with the IT deaprtment and nicely explain to them what you'd like to do. I know some IT departments like to keep ultimate control. I'm an IT tech in a small company and I see technology as a tool to enhance employee and company performance/service. My role is to make that happen not hinder it. Of course network security is important, but what you are asking to have done is easy to accomplish without any security issues.
Let me know if you need more info,
Dave