Another possibility.
The person speaking is not a philologist; it sounds like someone who regards anything before the nineteenth century as "antiguo". In fact the language referred to is almost certainly not Old Spanish (castellano antiguo), which means fifteenth century or earlier, since the earliest extant dramatic texts in Spanish (with very few exceptions) are fifteenth century. It quite probably refers to "Golden Age" (sixteenth- or seventeenth-century) texts, which are strictly in early modern Spanish. It might even be talking about eighteenth- or nineteenth-century texts. But as I say, the speaker is not a philologist; "antiguo" is inaccurate, and "old" is inaccurate in precisely the same way.
As for "castizo", I think this depends on the context. The basic meaning, of course, is linguistically "pure" or "authentic". From a Latin-American perspective, this probably would mean "Castilian": the "pure" variety. This translation would make less sense if the speaker is Spanish, since in that case he/she would not envisage putting the texts into non-Castilian Spanish. I think "original" would be quite a good choice.