Your old cables maybe better than many new cables you find. Copper metal is near record highs so everyone is cutting corners. There is lots of fake ethernet cable being sold.
You need nothing special cat5e cable can run full gigabit speed. Check the markings on your cable. There is a very slim chance it is cat5 (ie not "E"). It was not really being sold much even 10yrs ago so it is likely your cable is cat5e