for that price and feature set the odroid c4/c5 and the orange pi 5 (or 5b with onboard emmc) are the usual sweet spot. if you want zigbee i'd lean toward a board with proper usb (not just the otg ports some of the cheaper ones have) so your zigbee stick gets a clean port and a decent antenna position. one thing worth saying upfront from experience: skip the sd card for anything thats writing 24/7 like home assistant's database or pihole logs, you already know this but emmc or a small ssd over usb3 will save you a ton of corruption headaches down the line. and budget a few euro for a heatsink, the rk3588 boards in particular will thermal throttle in a closed case without one.
for the support angle werner's spot on, sticking to standard/platinum boards on the download page means kernel updates keep coming and you're not chasing a dead community image in a year. raspberry pi 4/5 is the boring-but-safe option if you can stretch the budget, just because the software ecosystem assumes it exists.
on the software side, since youre running pihole + HA + zigbee you'll basically be living in docker, which armbian-config can set up for you. if you ever want the rest of the self-host stack (nextcloud, file sync, vpn back in) without hand-rolling reverse proxy and certs, full disclosure im involved in an open source project called syncloud thats basically a thin layer that does one-click app installs and handles https/auth/updates for you on arm boards. its not for everyone, if you enjoy wiring up nginx and docker-compose yourself you'll probably find it too hands-off, but for a set-and-forget home box it takes the fiddly parts off your plate. either way the boards above will serve you well.
