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.

Only difference really between Intel vs AMD for self hosting is ECC compatibility. Personally, I tend to be picky about ECC for my server builds (all done on ATX systems thus far), so I go for AMD, but for smaller use case scenarios outside of ZFS pools it shouldn't matter a ton. If you go the AMD ECC route you'll have to set aside a spare GPU for local bios/terminal use (or go for the 4000 series pro version of Ryzen, can be had on ebay from resellers for decent prices). otherwise Intel and AMD don't differ function wise outside of ECC concerns, just make sure to match it with a chipset that will give you the lanes you need to allow for future expandability pcie-wise. (the expandability wasn't a concern when I first started, but as my self hosting needs expanded I had to replace a motherboard). can't comment much to wifi APs (I run pfsense and wall off my wifi on it's own vlan, I ran ethernet throughout the home and my wifi devices that need access to my main network tunnel through via wireguard)