Throughout the Roman period speakers were using consonantal patterns of a [w]-glide[17], perhaps becoming an unrounded glide and finally a bilabial fricative [β].[18] This Koiné innovation of [β] has also been included in Living Koine Greek as consistent with the decision on consonants....
The problem of pronunciation is a thorny one for both Latin and Greek scholars, so once you have chosen a system the best idea is to try and be consistent. I have a few undergraduate students who have gotten rather carried away with proper classical pronunciation…with occasionally humorous ...