Thank you both for the info - I'll pick up a screw to plug it.
I thought I'd post here (with permission) some of the info @Bettatail
was kind enough to share with me regarding the various components, with a little of my own commentary added.
When looking for a metering valve, be aware that not all valves are 1/8" NPT - some will require adapters (.e.g. Swagelok B-SS2 S-series). So a deal you find might not really be that much of a deal if you factor in the cost of said adapters.
Power consumption is an important factor for solenoids - every watt of power that the solenoid consumes goes straight to heat. Many solenoids are not meant to stay on for hours at a time, like they will be in our application. Finding a low-power (~2W or less) solenoid will protect you against possible damage from overheating. Clippard Mouse solenoids are usually the go-to here, although Bettatail pointed me to the Numatics LS solenoid (specifically, the LS03M6F00V) over a Clippard Mouse. Numatics HS solenoids are also good, even though they pull about twice the power of the LS at 1.5W (still low, so not a big deal). Keep in mind that with each of these solenoids there are TONS of different model numbers, some of which won't work or won't work well. Fortunately, people like @Bettatail
are very willing to share their immense knowledge on which models to get.
With a small solenoid like a Clippard Mouse or a Numatics LS you'll need a 12v power supply, which you can get on Amazon for $5-10 if you don't have a spare lying around the house. Pretty much any old transformer will do, at ~1W these only pull around 100mA of current. You can either directly wire the PS to the solenoid, or you can buy a female 2.1mm barrel jack pigtail
for $5 to connect to your solenoid so you can easily connect and disconnect power.
You'll also need a manifold to connect the solenoid to your plumbing. I believe the Clippard 15490-5 / 154905 (~$20 after shipping on Ebay) is the way to go here for both the Mouse and the LS. As mentioned above, if you have a 3-port solenoid, you'll need a 10-32 screw to plug one of the holes.
When assembling, use a drop of blue Loctite on all the post-body fittings except the CGA nut - use Teflon tape on that one (although be careful not to use too much or let the tape get inside the CO2 flow path.
Hope this helps. Please correct me if any of the above is wrong!