You may still be able to stream 4K video, as long as the video direct plays.
Direct playing video uses very little resources. It is essentially just reading the file from the disk and streaming it over the network. Unlike transcoding, there is no modification of the stream.
Install Plex Media Server on your PC and see what happens. It might work just fine.
Regarding transcoding:
Transcoding can occur in software or in hardware. Software transcoding uses the CPU. Hardware transcoding uses the GPU which may be integrated with the CPU or a discrete GPU add-in card.
Hardware accelerated transcoding in Plex also varies by the operating system:
- Windows: Intel Quick Sync Graphics (integrated GPU), Nvidia GPU cards, and AMD GPU cards.
- Linux: Intel Quick Sync Graphics and Nvidia GPU cards. There is no support for AMD GPU cards at this time.
Regarding your current setup:
The FX 6300 has no integrated graphics. Therefore, there is nothing Plex can use for hardware acceleration, irrespective of the OS.
With Windows, you may be able to use the R9 270 video card for hardware accelerated transcoding. It depends on the capabilities of the card. From what I can find on Wikipedia, it appears the card supports transcoding of H.264 video but not H.265 video. References below.
As previously mentioned, when running Linux, Plex does not support hardware accelerated transcoding using AMD GPUs.
So, with your current system:
Windows: You should be able to direct play any video. You can software transcode one or two 1080 streams. You can most likely hardware transcode H.264 video, but not H.265 video (references below).
Linux: You should be able to direct play any video. You can software transcode one or two 1080 streams. No support for hardware accelerated transcoding.
If you want to use hardware accelerated transcoding for H.265 video, including 4K, with your system, you need a different video card. A Nvidia GTX 1050 supports hardware transcoding of H.264 & H.265 video. The card is supported for both Windows and Linux operating systems. You can use a more recent AMD GPU card for hardware accelerated streaming, but only when running Windows.
Suggestion:
Install Plex Media Server on your current system and see how it performs. If it meets your needs, then you’re done.
If you need additional transcoding support for H.264 video, try a Plex Pass to enable hardware acceleration. You can try the $4.99 USD/mo subscription and not renew it if it does not meet your needs.
If transcoding H.265 is required, consider acquiring a Nvidia GTX 1050. They are available on ebay for under $150 USD.
If the Windows OS puts too much load on your system you can move to a Linux distribution. If you want hardware accelerated transcoding you can add an Nvidia 1050 or better GPU.
References:
What kind of CPU do I need? Note 1080p software transcode needs Passmark of 2000.
FX 6300 Passmark. Passmark = 4111
Using Hardware Accelerated Streaming
Nvidia Encode/Decode Matrix - look for cards that decode H.265 12-bit video.
Wikipedia: Radeon R9 270. Note use of Hawaii Pitcairn XT chipset
Wikipedia: AMD Unified Video Decoder. Note UVD 4.2 / Hawaii UVD 4.0 / Pitcairn has no H.265 decode capability.