Your budget is really near a https://store.ui.com/us/en/collections/unifi-dream-router/products/udr Unifi dream router. Your family is gonna be way happier with you (0 downtime) and it’ll give you extender options if you ever need it. Unifi is good enough and they update regularly, just disable cloud access stuff and you’re good.

Otherwise you want Opnsense instead of Openwrt. The upgrade process for Openwrt is not automatic, while Opnsense is. Worth it not to have to dote on your router.

And you should get an access point (Unifi something or Tplink Omsomething), wifi is problematic with openwrt and I’m not sure if opensense even lets you do it (haven’t tried).

And you’ll need a switch, dumb or managed, up to you if you want VLANs. The Opnsense box will have just one LAN port, so it requires a switch if you want to plug more than one thing into it. A switch with PoE+ can power the access point directly.

Opnsense needs x64 arch (Intel or AMD CPUs), get a small thin client like a Dell Wyse 5070 extended or HP T730 or that mentioned Fujitsu Futro S720 (its CPU is old tho, you can do better). There may be newer thinclients, you just want a mini PCIe slot to install some Intel gigabit card from eBay with 2 ports. Google power efficient gigabit mini PCIe card - there’s an older model that sucks power and a newer one that doesn’t suck; if you go more than gigabit skip 2.5 on Intel unless you google hard and expect extra power draw. Very limited point to 4 port cards, just go higher gigabit speeds don’t think about multiplexing ports or whatever it is called; and switches switch better than the router can and remove CPU overhead for more actual routing work - 2 port card is the way.

Slap Incus (superior but newer, less guides, LXD is previous name if googling stuff) or Proxmox (good enough, more guides for this) on it, make a VM and pass through the 2 ports of the PCIe cards, slap Opnsense in the VM. Make an LXC container and slap Debian on it and spin up the Unifi controller for your AP. Another container for adguard home or pi hole and you’ve got a box that does the basic nets all in one. The built-in port on the thin client is how you will access the underlying OS, it gets plugged into the switch you’ll have to get. If you got something with 2 gigs of RAM and an AMD Geode/GX or aged Intel Atom CPU I’d just only do Opnsense no hypervisor stuff.

Sorry for the info dump but there’s a lot of angles!

But really, the Unifi dream router is much easier and solves it all-in-one. You need 3 pieces (router, wifi access point, Ethernet switch) for a good experience otherwise.