PeterH has covered it all really. A few additional points - if you're going to use arduino, stick with the Uno if possible: it'll cover your initial needs, your students are bound to destroy some and the Mega is pricy.
While you're developing, consider a method of logging; when the prototype is in place and runs for a while and then crashes, it'll be useful for debugging purposes to have some record of what was happening. If you don't go the PC route for this, an SD shield will let you write logging data to an SD card - plenty of capacity for telemetry.
I assume you're already considering some starter kits - I'd expect the class to start with flashing a led and working piece by piece towards the greenhouse controller. It'll also enable your educating yourself to the point of being able to help debug student's efforts. For a classroom situation, for cost reasons, it may make more sense to buy discrete components.
Consider some kind of greenhouse simulator, even if you're just using potentiometers and leds. That way you can test for a variety of conditions more quickly and ensure that the controller acts correctly without having to go to the greenhouse and wait for conditions to be right. Over time, you might be able to develop this into a complex project in its own right, with a web page controlling it and/or standard scripts that run the prototype controller through a set of scenarios and reporting on its performance.