so.. you're running debian minimal with no window manager then just invoking chromium via commandline and browsing to a web app?
Exactly, That's the smallest (AKA cheapest) setup I can think of.
you might also try flint os, the active chromium os build
https://pimylifeup.com/raspberry-pi-flint-os/
or running a light wm like xmonad / i3wm instead of just running from command line using x depending on the functionality you want http://www.alandmoore.com/blog/2011/11/05/creating-a-kiosk-w...
The server is remote