ratpoison (https://www.nongnu.org/ratpoison/) is a keyboard-driven window manager (wm) and if later you find that Nyxt isn't the web browser for you, then I'd also check out uzbl: https://www.uzbl.org/
I would definitely use webkit because there's shittons of behavior in the engine that is going to be really difficult to replicate and without it no one will use your browser. Also it needs to be dang fast. Seriously, writing a browser engine from scratch is probably a good 100 engineer year project at least. And all the fun stuff will be on top of it.
In terms of what I would actually write? It would be basically https://www.uzbl.org/ .
I use Vim Vixen for Firefox, but one thing that bothers me is that a blank tab and pdf document doesn't seem to have the keybindings. So if I land myself on one of those two tabs I can't do things like press d to delete tab or move to another tab. I have to get my mouse and click. Which I know is a bit of a lame complaint, but if I'm gonna use a keyboard full time I wanna use it full time, you know. That's the problem with plugins like this, it seems they can't quite fully cover of all firefox's features.
I've been wanting to find a good browser that's built from the ground up to use a keyboard, that way it shouldn't run into issues like this. I have not yet tried qutebrowser, although I should. I hear it has issues with youtube videos and stuff? Maybe someone can give more info on that.
There's also the surf browser, but man patching suckless programs can sometimes be a pain. You can 100% modify the keybindings on this one btw. I'm not sure if it'll work with every site like a modern browser.
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Lastly, I found this browser in case if anybody is interested:
Pretty cool sounding browser. I installed on my Arch Linux install, I installed from source, and it didn't pull all the dependencies so had to install python-wheel and python-pip. But it still doesn't work. It has this thing called an event manager that fails to launch.