Skillie:
I am very happy with Plex Media Server (https://www.plex.tv/) - easy to setup - many cool features - supports various file formats, devices, platforms etc.
Why do you say it is "too slow"?
Plex's transcoder isn't a "turd". Video transcoding is fairly processor intensive, and you need a relatively decent system to do it in real time, especially if you are serving up HD content and/or multiple streams at once. I'm running Plex on lowly powered 2.13Ghz dual-core atom NAS, and it works fine. Provided the client can direct play the files without transcoding, it works very well.
Coming back onto the OPs question, I recommend against using a Blu-Ray player as a client. They typically aren't that good - with clunky interfaces, limited codec support (forcing your low-spec server to try and transcode) and a generally crappy user experience.
My downstairs TV (Samsung, 2015 model I think) has a plex app, and is easy to use. Lovely experience.
Upstairs, it's not so great. I have a dumb TV. I have just ditched the client I was trying (android box) as I never got it to work right, and it was becoming a PITA. The elderly WDTV Live I was using worked well, but the user interface was awful after having the proper Plex one downstairs. I have ordered a Raspberry Pi 3 with a wireless to replace it, and it will either run Rasplex or PlexKodiConnect. I am trying it because its inexpensive, and gets good reviews viz., capability and usability. I will have it in a week or so, and happy to post a follow up once I have it working.
Personally, I like Plex. Having the episode synopsis, and posters makes for a nice and GF-friendly user interface. And being able to filter by actor, genre, rating etc is pretty nice. Emby also gets good reviews (I haven't tried it), as does Kodi (which I haven't tried either, but you apparently need to faff around with MySQL to get a good multi-room experience, and storing the metadata centrally also apparently requires some fiddling). But none of these gets around your central problem - you either need good clients and/or a good server. If your client won't play the material natively, and your server has insufficient horsepower to transcode for the client, then you won't have a good experience.
Any of Plex, Emby or Kodi should work well with a bit of tinkering, provided you have hardware that is up to the job.