A solution could be to put another layer on top of the internet. This could be done by means of a "presentation proxy", similar to cloud gaming, e.g. based on VNC, where only a VNC client is run on the old computer, and the browser is running on the presentation proxy.
That still leaves the attack-surface of browser-based activities (do you really want your recreational activities sites interacting with your financial services?), but both gives the option for fresh respawns (OS and/or browser) and physical and network isolation of your local storage and data from your browser.
(This presumes hygiene on any browser-based downloads as well, of course.)
In general, the idea that we'd want all our data on a globally-accessible network is seeming increasingly unwise to me over time, given both technical and political developments.
Late edit: Oh, and Browsh: text-only browser-via-proxy supporting CSS/JS.
My non-tech friends call me paranoid at the basic level of protection I do - separate browsers for everything, and a couple of VMs for e.g. finances.
Vlan has always been an important part of LAN security but we're just out here with always on, full Internet access? My home firewall logs show an insane amount of bot / scraping etc.
I usually I just go to archive.is and read the page there.