What are the fundemental differences of different Bluetooth modules for beginners?
As far as simplicity is concerned, HC05 would be the way to go. It is by far the most popular and there are a tonne of tutorials on using it (just a quick google search). As for the differences:
The HC-05 module can build a connection to other modules. E.g. a Robot being a master and connecting to slave bluetooth module. Or in slave mode to make a wireless bridge to a notebook.
The HC-06 module only can be a slave. This makes it only useful for say connecting a notebook as a master to a robot with a slave module e.g. for a wireless serial bridge.
As for the HC07, support seems low so I would recommend sticking with HC05 or HC06
At the end of the day it comes down to your requirements. If you are only wanting to talk between the phone and your arduino than the HC06 would work fine, however if at some point in time you want to talk to another arduino, than hc05 would be the way to go.
I don't really know the differences but I've used the HC-06 modules. They are slave-mode only but that is what you need to replace a hard-wired terminal to your Arduino, such as your PC and and a USB cable, with a Bluetooth terminal. That probably covers 99% of cases where an Arduino or other MCU-based device needs to communicate to a PC or tablet that already has Bluetooth built in. For device to device communication, one of them would have to be a master, and I think that requires an HC-05.