Suggestions for converting incompatible file formats

Hi Everyone,
I’m just getting a Plex server up and running, and would like to include my movie library which includes lots of BluRay (BDMV and other folders) which Plex doesn’t work with.

Would like to remux these into compatible MKV type files, what tools are the best to do this?

Would it make sense to transcode them? I’ve got a new HTPC that has decent performance (Intel i5 -8400 CPU, NVIDIA GTX 1060/6 GB VRAM, 16 GB RAM, 2 500 MB SSD, ASUS ROG Strix-I mobo). Using Diskstation NAS for storage of media files.

Thanks for advice.