Hi Colette, and welcome to the Dev Forum!
The C++ compiler that comes with Mac development tools is gcc 4.0.1 or higher, which is the most popular compiler for Unix and Linux. gcc is also available for Windows, however most Windows developers will be using Microsoft tools. In particular they'll be using Visual Studio as the Integrated Dev Environment (IDE).
The IDE for the Mac is called Xcode, and it's quite different. If your class is using an IDE, it will probably be more important to have the same IDE as everyone else than to have the same compiler. The IDE includes the text editor you'd use for all your coding as well as numerous other tools. You won't want to be using Xcode if the instructor is constantly referring to particular features of Visual Studio.
On the other hand, many programming classes don't involve any IDE, since that interface really has nothing to do with the actual programming. In fact many University classes will be using a text-based interface to Linux. In that case the compiler will probably be gcc, and your Mac environment will be almost identical to the school's environment.
then use the same SW as everyone else.
Do you know what that SW will be? That's the key question. Also find out if you'll be expected to install the compiler, etc. on your computer or whether you'll just be using your computer to login to the school's network to use tools running on the school's computers.
I think the worst case would be if the class is using Visual Studio, and the best case would be if the class is using a text interface to gcc running on Unix or Linux. Most non-Mac users have no idea that the Mac Terminal application provides almost exactly the same interface as a Unix terminal.
will I have complete support (like when using the Personal Training team), to help me with C++ compilers?
If the class is really about programming and not about pointing and clicking in an IDE, C++ is going to be the same regardless of the compiler. If your tools are different, the level of support you'll get will depend on the experience of the staff. If any of them are real programmers they won't even notice that your warnings and error reports look a little different from the other students.
If you can find out what the computing environment will be, someone here will be able to give you good advice, ok?
\- Ray