Any old spare PC will work fine provided it has a spare PCIe slot.
In the following sections, I describe two ways of building something much smaller than a normal PC, using an HP thin client or a Lenovo Tiny desktop.
The HP T740 thin client is available on eBay for about $200. It is unusual in that it has single PCIe slot that accepts standard low-profile cards on a standard low-profile bracket, while being only 2.2L in size. It also has an M.2 wifi slot.
There's a review on ServeTheHome.
It comes with an eMMC card, but I wasn't able to boot from this after installing Linux. I installed an inexpensive M.2 NVMe card in place of the eMMC card and that worked fine.
I had a problem with the BIOS not detecting the CPU fan on boot. This was fixed by upgrading the BIOS. Upgrading the BIOS required downloading and running a program on Windows 10 (Windows 11 didn't work) to create a disk, which the BIOS could use to update itself.
This shows a T740 with a cable attached to the i210, before plugging the i210 into the PCIe slot.
Some Lenovo Tiny desktops have a slot into which you can put a riser that accepts low-profile PCIe cards, but without their bracket.
I recommend buying a second-hand M720q. These are widely available. Try to get one without a wifi card, because we will use the wifi antenna hole to connect with the GPS or i210 card. It should also work with an M920q or M920x.
There's a review of the M720q on ServeTheHome.
The M720q has space for a 2.5" disk (usually an SSD), but you cannot use this at the same time as a riser. So you will need to remove the 2.5" disk and install an M.2 drive (there is space for one under the bottom cover).
You will also need to get a kit which has the riser, a cover plate with an opening (sometimes sold as a baffle or a bezel) and some screws. The Lenovo part number is 01AJ940 (this is just the riser, I believe). These are available from AliExpress or eBay (search for 01AJ940).
The cover plate is designed for a 4-port i350 card. This means that the opening is bigger than necessary for a single RJ45 card. More importantly, the cover plate has a clip that is designed to retain a low-profile card that occupies the full-height of the low-profile bracket. The i210 card is shorter and so the clip does not work to keep it in place. Improvisation is therefore necessary to keep the clip in place.
The rear of the PC has a small hole that can accept an SMA female bulkhead connector. In models without wifi cards, the hole is covered by a disc with a little slit, which can be pushed out with a screwdriver. We can then fit a pigtail with an SMA female bulkhead into this hole.
This shows a build using an i210 and the ArduSimple M.2 card. There is U.FL to SMA female bulkhead cable going from the rear of the computer to the antenna input on the M.2 card. The i210 is fitted with the breakout board from Timebeat. I've put a piece of Kapton tape on top, since the breakout board can come into contact with the case (electrical tape would probably have been better). There is then a U.FL connector going from this breakout board to the PPS connector on the M.2 card. I've improvised a way to keep the i210 in place using a couple of pieces cut off the corner of a stripboard.