Here's a 25U Open Rack Cabinet on Amazon for ~$230. Barring buying new, maybe troll your local Craigslist - sometimes racks turn up there.
Not sure what your total budget is for this project, but I'll lay out my thoughts.
For Plex, your CPU requirements will depend partly on how many devices you are streaming to at a time, and whether or not you need to transcode your streams or not, as well as the quality of your 4k files especially.
Here's a quick breakdown from the Plex Website
The most basic thing to remember is that the more Plex apps you have playing content at the same time, the more CPU power you’ll need. Generally speaking, if you have two Plex apps requiring transcoded content at the same time, that will require about twice the CPU processing power compared to if there was only one app playing content.
If you want very basic minimum suggestions:
No transcoding: Intel “Atom” 1.2GHz (NAS devices based on ARM processors should also be capable of at least one stream with no transcoding)
Single 720p transcode: Intel Core i3 3.0 GHz
Single 1080p transcode: Intel Core i5 3.0GHz
Single 4K transcode: Intel Core i7 3.2GHz
If you’ll need to support more than one simultaneous transcode, you’ll need a more powerful processor.
Very roughly speaking, for a single full-transcode of a video, the following PassMark score requirements are a good guideline for the following average source file:
4K HDR (50Mbps, 10-bit HEVC) file: 17000 PassMark score (being transcoded to 10Mbps 1080p)
4K SDR (40Mbps, 8-bit HEVC) file: 12000 PassMark score (being transcoded to 10Mbps 1080p)
1080p (10Mbps, H.264) file: 2000 PassMark score
720p (4Mbps, H.264) file: 1500 PassMark score
The CPU Benchmark website is a good resource to see what sort of PassMark score a particular processor received.
You can see that CPU requirements for 4k is still very hefty.
You might do some research to see if a video card might help with transcoding. I'm not really up to snuff on that side of things. I do not have 4k media on my Plex server, so I can't speak to experience on this, I'm just giving what info I can.
Anyway, all that follows below assumes you are relying on CPU only for transcoding.
The Passmark Score for 2x Opteron 6274's (2.2 Ghz 16 Core) is 10536
According to Plex's guidelines, that may or may not get you 1 4k stream.
I might suggest looking at this site. I have no affiliation with this site. I gain no benefit from recommending this site, it's just a good deal.
This site talks about builds built around a dual Intel Socket 2011 server board available for $175. It can take 2 Intel E5-26xx v1/v2 processors.
It still takes DDR3 Memory. It comes with 2 10GB ethernet ports on board, and as well as a built in 8 port RAID Card.
Right now, you can buy that motherboard, 2x E5-2650v2 Processors and 32GB of ECC DDR3 1600 Mhz Memory for ~$400 Dollars.
Those 2 E5-2650V2 Processors give you a Passmark score of 18988
They are also newer processors than the Opterons and draw less power.
You also have a lot of other processor options for that board. Any Intel E5-26xx V1 or V2 processors should work.
A lot of those chips can be found cheaply on Ebay.
I personally have 3 servers (Not using this board) running E5-2670 V2 chips. They are 10 Core processors. I picked them up for about $150 each on ebay.
The highest end chips you can put in that board are either E5-2697 v2 for core count (12 Cores @ 2.7 Ghz w/ Boost to 3.5) or E5-2687W v2 for Core Speed (8 Cores @ 3.4 Ghz w/ Boost to 4.0)
2 E5-2697 v2 gets a 23334 passmark score
2 E5-2687W v2 gets a very similar 23319
Note that those chips are still much more expensive used (Looks like E5-2697 v2 are going between 3-$500, and E5-2687W v2 are running 3-$400, but they do give you a bit of an upgrade path, if needed.)
If you need more CPU power than that, you'd have to look for something newer.
Alternately you can always go lower on the stack as well.
Here's a link to the Intel database for E5 V2 processors. Note that it also includes E5-46xx chips, which are not compatible with the above board.
A few other things to think about in comparison to the above in terms of rough CPU equivalency...
An Intel i5-9600k gets a passmark score of 13455
An Intel i7-8700k gets a passmark score of 15968
An Intel i7-9700k gets a passmark score of 17269
An Intel i9-9900k gets a passmark score of 20152
A Ryzen 2700X gets a passmark score of 16987
A Threadripper 1920x (1st Gen. 12 Core) gets a passmark score of 19937
A Threadripper 2920x (2nd Gen. 12 Core) gets a passmark score of 22053
A Threadripper 1950x (1st Gen. 16 Core) gets a passmark score of 21914
A Threadripper 2950x (2nd Gen. 16 Core) gets a passmark score of 25648
If you have more questions, fire away and I'll see what I can answer, and maybe someone else will chime in too.