Which operators must be overloaded by this custom string class

A custom string class - MyString - has a one parameter default constructor, a copy constructor, a move constructor, and a destructor. These special methods of MyString manage memory, copy, and move the string data as required.

class MyString {
 public:
 /* Default Constructor */
 MyString(const char* str=nullptr);

 /* Copy Constructor */
 MyString(const MyString&);

 /* Move Constructor */
 MyString(MyString&&);

  /* Destructor */
 ~MyString();

  /*
    Overloaded Operators ??
  */

 private:
 // Pointer to string's location
 char* m_str; 
};

Consider following usage of MyString:

std::map<MyString, int> mstrmap;

mstrmap["One"] = 1;
mstrmap["Two"] = 2;
mstrmap["Three"] = 3;
// -- More Elements -- 

Taking into consideration above usage of MyString as a key in std::map and dynamic-memory management in MyString, select only those operators that should be overloaded in MyString: