Inheritance or lot of relationship?
This is just a common answer.
Avoid MYSQL for OOP Concepts for the time being. OODBMS stil under research in some areas.If you are Maping OOP business/program logic to a RDBMS(ORDBMS)  and still expecting open source go for PostgreSQL(PGSQL). PGSQL is not a full OODBMS. But Inheritance can be achieved there.
Your methods may result in unusual processing cycles thus results in excessive workload to the system. If you are going with your methods (In between Helper Tables ), make sure you using correct Indexes.
And, still if you are preferring MYSQL, Use High level of Abstraction to achieve Specialization down the Inheritance hierarchy and link via Foreign keys with parents. Do Normalization  up to 3NF correctly. Yes! this is the usual Relational Way!!