Well, the browser could choose not to download the images, videos and styling information. Trouble is that many modern sites load their content through JavaScript programs that can be comparatively massive.

But I guess losing those sites would be a small price to pay for OP.

Just loading the text should be really small, especially when it is compressed, which should be the standard nowadays.

The rendering speed difference is negligible, with a bandwidth this limited the only strategy is to limit what the browser fetches. You don't need a proxy server to strip out page content (also because that would imply breaking the encryption stream), a browser could simply choose not to fetch any image or multimedia resources, override remote fonts with local ones, etc. In that sense the choice matters, because some are specialized for this purpose or can be configured to act in these manners

Is there ways to do it on firefox, i remember opera had this gimmick.

I needed something like this back when I lived out in the sticks. Could only get 2g - 3g on Verizon at home, had a DSL line for the desktop, high speed connections were prohibitively expensive. Back in the day you could just walk away and let sites buffer while doing other stuff, but as the rest of the world grew faster, low speed customers got left behind. Everything is set to timeout if it fails to load in a couple minutes.

Only solution I ever found was to disable JavaScript, force everything to HTML/CSS only where possible, and use a download manager with automatic retry/restart to download any videos I wanted to watch from YouTube or Facebook.