I want to setup a headless single board computer (SBC) to run things like iobroker for Eufy Security interface to HE, NUT for battery backup monitor, pihole, etc. I don’t need any extra features like WIFI, camera interface, dual monitor ports, audio port, etc.
Can a single SBC run these multiple applications simultaneously? What specific hardware model (e.g. rPi, Audrino, NUC, etc) should I buy?
RPi’s have the largest userbase. I don’t consider Intel NUCs to be traditional SBCs, but they come with the benefit of running Windows if you need that.
Personally, I like Hardkernel’s hardware, so I’ve used Odroids for a long time.
Raspberry Pi's are hard to find at a reasonable price. Good luck. Rpi Zero 2W would work except you said you don't want wifi. Avoid the Nvidia Jetson even if it is cheaper than it used to be.
Odroid N2+, the board recommended by @erktrek fits that bill. I bought one 2 years ago for about $80. You could also find an RPi 4B+ for that price range.