Thank you for all of the photos, they certainly help in identifying the compressor and gives me an idea of what you need.

You'll certainly need a Pressure Switch. Since this is a two-stage unit and has a maximum operating pressure of 175 PSI (which is typical for 2-stg units), I'd recommend a Pressure Switch rated to cut in at 145 PSI and cut out at 175 PSI.

You can view our Pressure Switches by clicking on the below link. You really just need to choose your cut-in and cut-out PSI settings, whether you need a "single-port" or "four-port" manifold and an Unloader Valve or no (most systems do require an Unloader Valve, which would have an Unloader Line routing to the side of the Check Valve or to the pump head):

SquareD Switches: mastertoolrepair.com/pressure-switches-s...ches-c-25_2_328.html

Furnas/Hubbell Switches: mastertoolrepair.com/pressure-switches-h...ches-c-25_2_256.html

The Check Valve in the main tank inlet looks like it'll be a 3/4" or 1/2" male NPT fitting. If the ID of the tank inlet measures 3/4" then you'll need a 1/2" MPT check valve (always subtract 1/4" from the ID of the female thread in the tank to find the size of the male fitting that threads into it).
I'm not sure what the outlet type of size is, you could install a Check Valve with a male compression fitting, female NPT fitting or flare fitting.

You can view our Check Valves by clicking on the below link:

mastertoolrepair.com/air-compressor-part...k-valves-c-25_4.html

For the Pressure Relief Valve, I'd recommend a setting of 200 PSI, and 1/4" MPT threads. This would be our "SRV250200" which you can view by clicking on the below link:

mastertoolrepair.com/safety-valve-200-psi-srv250200-p-361.html

For the Drain Valve, I'd recommend this heavy duty 1/4" MPT drain valve at the below link:

mastertoolrepair.com/drain-cock-brass-he...hes-132a-p-1055.html

For the tank Pressure Gauge, I'd recommend the below standard 1/4" MPT bottom-mount Gauge at 300 PSI:

mastertoolrepair.com/pressure-gauge-pg0250300bt-p-330.html

BTW, I uploaded a manual for this 310 25 Quincy compressor for your reference.

Hope this helps get you started!

- MTR