CPU for DIY NAS

Very roughly speaking, for a single full-transcode of a video, the following PassMark scores are a good guideline for a requirement:
■ 1080p/10Mbps: 2000 PassMark
■ 720p/4Mbps: 1500 PassMark
■ The CPU Benchmark website is a good resource to see what sort of PassMark score a particular processor received.
■ You can also try doing a search such as "FX 8300 passmark" on Google or similar to help you find information for a particular processor.
■ Basically, if you think you may be needing to handle 4 simultaneous content streams and they might all be 1080p content that requires transcoding, then you would take the base guideline (2000) and multiply it by the number of simultaneous streams (4) to get your rough requirement, which would be a PassMark score of 8000 in this case.
In this example, that means you would want to look at processors with an 8000 score or higher.
■ Also, keep in mind:
If you'll be using your computer for other things beyond simply running Plex Media Server, you'll want to make sure you have some extra power so that you can continue performing other tasks
■ It's a good idea to remember that your usage today may not be the same as your usage in the future. You never know when you'll get a new device to run Plex, share content with a friend, etc., which could all result in more usage.
■ Generally, it's better to opt for a faster CPU than more RAM. It's easier to add more RAM to empty slots than change the CPU. If the CPU is not powerful enough to keep up with transcoding the media, you will notice the player App pauses every now and again as it waits for the Server to catch up. This pausing is a sign that the CPU is not powerful enough. If the OS becomes low on RAM, you may also see some pausing
■ FX 8300 has score of 7617 which is able to stream 3 1080p videos at the same time with some room for other things .
Core i3 4170 has score of 5186 which is able to stream 2 1080p videos at the same time ; any additional loads of streaming 1080p or encoding it will cause pause in the streamed videos .

however FX 8350 has much much better score of 8979 which is able to stream/transcode 4 1080p videos at the same time with some room left for small loads .

4K is double 1080p so you need a passmark score of at least 4000 to stream 1 video safely
You need any gpu to go with the FX 8300/8350 as they do not have integrated graphice
You can go with a low gpu and put all the load on the CPU , or you could go for a mid gpu that supports h264 decoding to help reduce CPU usage ; depends on application to run CPU/GPU decoding ; this will not benefit streaming , go with a mid gpu ONLY if you want to watch(video playback with a player app) a video on the server WHILE streaming other videos to other devices
So you must go with FX 8300/8350 to be able to do what you need

any cpu will be enough for NAS ; but you need good motherboard RAID support if you will use RAID in your NAS ; if you will go with non raid setup then it's fine.

I suggest using the GA-970-UD3P (rev 2.0) board as it has enough power delivery to the CPU ; if you use a cheap board with FX processors it will burn .

You might also need to get a cooler for the CPU ; you will put much load on it