Not sure why you think it would be an infinite loop? Each variable only has a set amount of values and is evaluated exactly once. This is in turn assigned to what is on the LHS of the equation.
As for should you include your HOME path in your PATH variable I would consider the fact that of all the places where it is easiest for malicious commands to reside would be in a user directory,
I would not personally place it in the PATH at all.
As with all versions of linux though, the choice is completely yours