Someone got their Mac Plus online with the help of a modern computer: http://www.keacher.com/1216/how-i-introduced-a-27-year-old-computer-to-the-web/
My PowerBook G3 works comfortably, but my Macintosh SE can't even load a single picture. What do you think is the oldest Mac (with upgrades) that can surf the internet?
If you don't need the pictures, then a 512Ke could probably connect using MacTerminal via modem to a dial-up remote Unix system (are there any of those left?), and run lynx in VT100 mode for text-mode web surfing. In lieu of a finding a remote Unix dial-up, a serial-to-USB plug on a raspberry pi might work.