So, for example a PDP11 running 2.9BSD (e.g. a 11/70 from 1975) should suffice, but there are other machines of similar vintage that support IPv4. You can also try putting a virtual PDP11 on the net using the simh emulator (http://simh.trailing-edge.com) and 2.9BSD from TUHS (https://www.tuhs.org/Archive/Distributions/UCB/2.9BSD/).
If you want something to run an IP stack, then a 286 running `ka9qnos` is about as small as can do hardly anything useful, probably. There might be a c64 IP stack but at that point its getting technicality again; how much access and function counts?
If you're looking for paranoid security in cheap hardware, 486 for absolute purists (runs linux handily, good luck with the graphics, matrox card ruled), and up to .. ppro? p3? or so if you're slightly less pure.
Or get Sparc 5 or alpha or etc "exotic" hardware of that era and have an extra layer of obscurity plus years of unpatched security holes in any software you can make run today.
Edit: Those remote jobs were most likely batch jobs, and I am not sure how they got the stuff over, may not have been over a network connection.
Thank you for the replies though, something to read up on.
is too broad. A C64 with a modem can access IRC and BBS
> minimal modification/add-on
This is a bit broad too. Every modern "add-on" has more power most of the old computer they are attached on.
You could run a proxy on the add-on, that would shrink pictures, html and remove https.
Or even simpler. The add-on could do all the computation and just use the old hardware to show the result.
Most computers built after 1980 should be able to do it with some tinkering. Pretty much anything built after 1990 should be fairly trivial to get online.
If you want something somewhat usable, then Lynx/Links running on whatever a modern Linux distro can boot on should suffice.
I used a modem to get online with my Amiga 600 (7 MHz 68000, 2 + 4 MB RAM) in the 90's. It was perfectly possible to use things like IRC, eMule and a WWW browser on it, but the modern web will be quite unusable with aMosaic...
https://en.wikipedia.org/wiki/Xerox_Alto
Ethernet and the Alto both can from PARC.
At a minimum, you're looking at as old as the 68020 Macs and the 386 PCs. The PDP-10, PDP-11, Amiga 1000, the earliest Sun machines (68k, pre-Sparc), and similar age machines from the 1980s and early 1990s having a really reasonable amount of functionality with the right options, OS version, drivers, and software.