How should I wire / connect a new ceiling light to this ceiling junction box?
Do you have a non contact voltage tester? Or volt meter? I would test the single brown to see if it is switched.
This may work like the single brown and single white, taking white to the white  to the fixture  and the brown to black the bare copper goes to the green.
Would be my first shot at it the black tape on the brown would be the hot going down to the switch the way I wire in conduit the tape is to remind me where the hot is.  If you have a tester or meter I would check the brown to verify it is switched but if not make the connections with the breaker off and give it a try.