I use plex on almost everything (Smart TVs, PS4s, Laptops, mobiles, iPads), and I have it in a big house with so many people using it. It runs very smoothly but cannot run H.265 files at all on any player.
Now I wish I can say I understood the bolded part, but I think the best way is to build and I would like to know how much roughly should I budget for it
Ok so this is the setup:
Synology NAS with Plex Sever installed.
Clients - PCs, TVs, PS4, Mobile -> ie the whole range.
Now if you stream without transcoding H.265 video to any of these clients, they will struggle to play it since they do not have a hardware decoder and their CPU is not powerful enough to decode it on the fly via software decoding.
Since you have multiple clients, building a box that would decode H.265 on the fly is not going to work - as that would be a single client.
What you need then is the Plex Server itself to re-encode the H.265 video to H.264 which the clients can then easily decode via hardware decoding. The only advantage here is that media is stored in H.265 which takes up less space. The bitrate will still end up being higher once converted to H.264 and sent to the client - So dont use this approach if we are looking to overcome a bandwidth issue.
I think a fairly beastly Plex Server would be needed to convert from h.265 to h.264. Probably looking at a i5 6600 - hard to say as i cant test it, nor find many people doing this.
Plex does support transcoding H.265 to H.264 - have you enabled this and tested the performance (figure out if the NAS is too slow or the Client).
What kind of source H.265 content do you want to stream? 1080p/4k? Approximate bitrates?