It was my first time seeing such a serious play, and I had a valuable experience.
Literal
This-kind-of serious play [obj-を] see [nominalizer-の] [topic-は] first-time [copula-で] valuable experience [obj-が] could-do [polite-ました].
初めてで uses the copula conjunctive で to chain 'it was my first time' into the next clause. 貴重な経験ができた uses the potential-like construction 経験ができる 'to be able to have an experience,' where the experience is framed as something that naturally happened to the speaker rather than something they actively did. シリアスな is the English loan 'serious' functioning as a na-adjective.