4u of space is less volume than many PC cases. I’ve got a 22u “half rack” in my apartment (half for testing gear for work, half because I like to tinker). Bigger concern would be noise. 1u network gear tends to have high pitched 20mm fans which can drive you nuts if you don’t have it in a separate room. Noctua makes a great kit I use in my own gear but Verizon probably wouldn’t be very happy with you if you tried to do that :).
I went the route of “find a dirt cheap gigabit colo” ($150/m for quarter rack with gigabit and bgp peering) and just tunnel the IP space back home. Upside is you don’t have to pay to have the circuit put to where you currently live and you don’t have to worry about space/noise. Downside is if you want to use it locally at home you get extra latency due to the tunnel.
If your use case is just to use the unique space locally then you don't need BGP at all but the second you want to use it elsewhere you incur the latency of going through the tunnel.
Currently I'm doing BGP over a wireguard VPN back to a couple of VPS providers. Actually, I only run OSPF to my home, the BGP part only happens on the VPS side. The tunnel does add about ~8 ms of latency worst case.
I went the route of “find a dirt cheap gigabit colo” ($150/m for quarter rack with gigabit and bgp peering) and just tunnel the IP space back home. Upside is you don’t have to pay to have the circuit put to where you currently live and you don’t have to worry about space/noise. Downside is if you want to use it locally at home you get extra latency due to the tunnel.