What model of modem/router hardware does the community recommend for hosting a reliable staking service? Are there any additional hardware or network configurations that are better for providing a service like this?
Assumption is that you are looking to host over a consumer broadband connection. If so the minimal thing you need to be able to do is configure port forwarding to your relay node.
However I would recommend to run a DMZ configuration to keep the relay and core node away from your home network. Therefore you need a router/firewall that can support a separate DMZ. Most consumer grade routers don’t do this so you need to look at semi-professional kit like Ubiquity. The EdgeRouter X is the entry grade model that has 5 x 1Gbit ports and will support stateful firewall rules, has SSH CLI and browser UI, and will support true 1GBs wire speed with hardware offload enabled. You can buy them on eBay for about $50-100.