Intel and AMD are so similar, they may aswell be the same platform. The only real difference is the iGPU where Intel has an edge in terms of transcoding quality.
I wouldn’t buy anything new or recently released for a modest home server. I don’t think you can get really good deals on alder lake CPUs yet, so I don’t think you need to worry about efficiency cores.
Any CPU made in the last decade or so can do virtualisation just fine.
I haven’t looked into this in detail yet but, for WAPs, I’d buy something that can run OpenWRT.
For firewall/gateway, it highly depends on your internet connection. If you have fiber terminated to copper, you could use anything that has an Ethernet port but with DSL or DOCSIS, your only reasonably choice is likely a SOHO router. In that case, I’d also look into getting one that can run OPNSense or OpenWRT depending on your taste.