Hardware advice for 2021

Optiplex 760 has a parallel port, so if you plan on starting with it, get that. The others will do just fine for ethernet mesa boards, some do have PCI or PCI-E slots.
HP8300 is for ethernet only.
Some Fujitsu also come with a motherboard header for parallel port, so a 5$ cable/bracket is all that is required.
Memory, for the official release of LinuxCNC that is based on Debian 10, 4GB of RAM are enough, Mint with Mate desktop will work fine with 4GB, but 8 would be better. 16GB are overkill for everything regarding machine control, but if you also plan to do CAD/CAM on it, it comes handy.
I never even tested any i3, i avoid them as the plague, but i5 and i7 worked just fine.
Same for the integrated graphics, Intel works in most cases, but i am aware that some chipsets have issues with a Linux driver, even those can be used by blacklisting the offending driver or using "nomodeset" at boot time.
After everything above, you are buying a used PC, so be prepared for disappointment as they might come with a variety of issues, from annoying to plain unusable.
There are 4 used PC shops in my town, i bought over 40 of those old PC's from 3 of them and never ever had any issue with them, the 1 remaining shop i got 4 PC's and all of them had issues and were utterly unusable.

I think I will be jumping in on this also, as I think I need to replace the PC in my VMC. I would much rather buy new, it does seem like much of the new hardware is not terribly happy with Linux on it.  It would be nice to be under $1000.

Jake wrote:

It would be nice to be under $1000.

OK
Asus ROG STRIX B550-i Gaming ~200
Ryzen 5 5600x ~230 >>I have a Ryzen 7 3700X
2X 16GB HyperX DDR4 3600 dual rank RAM ~240
1TB Kingston NVME SSD ~120 >>I use a 32GB NVME, yes 32GB !
Seasonic 500W SFX Power supply ~170
Cooler Master NR200P case ~110
Cooler Master MasterCool 240 Lite ~90
4X Arctic P12 PST CO fans ~35 for 5, the stock cooler master vibrate a lot
Optional : Saphire "reference" AND Radeon RX 6900XT ~2300 << I did not pay for this, i did for the rest, took over 2 months to gather the money!
Might want to change the processor to Ryzen 5 5600G or ryzen 7 5700G as they have built in graphic cards that put intel to shame, the first is the same price as the above, the second should be under 300 i think.
Sans the 6900XT, the economy would be
2X8GB DDR4 3200 RAM ~60
500GB Kingston NVME SSD ~55
Corsair 500-600W SFX power supply ~120
Arctic cooler, 120mm or 92mm, ~28-35
The good thing about the fans mentioned above, this is in my bedroom mining 24h, and i can sleep!
.. and work on two big monitors while it is mining. Does not like Freecad and susperslicer though, so i have to stop mining when using those two

I may be shopping tonight.....

That actually looks pretty close to my current desktop....

Ryzen 7 3700x
Asus Tufgaming X570
Corsair DDR4 64G
Samsung EVO SSD's
Noctura Fans (which are AWESOME.) Nearly silent. Almost has that gentle sea sound as they accelerate and decelerate.
Fractal case
Radeon Pro WX graphics
Corsair 750w PS

The only thing this new one will get used for is on the VMC, which only gets used for it, modifying some NGC's.... I am not size constrained at all I have like a 3' wide 2' deep 3' tall spot in the cabinet this tower can get placed into.

I come back in the house and use the machine in the office when the cad work breaks out.

That is a nice machine !
BTW, i do have a Noctua NH-D15 collecting dust ATM. And i have a Creality CR-10S Pro V2 with all fans changed to Noctua 40x20! They are silent for sure, but no one mentions that they move less air as they spin slower.

That is part of the reason I went with the larger tower on that machine even though I didn't need it. Just to have more volume of air available. Yes the Noctura does have lower air velocities, minimizing the turbulent flow is the key for the sound.

I'm going to have to do something fairly quick as I need to have the mill running.