I try to use the keyboard for everything but unfortunately I haven't found a proper plugin for modern browsers. I tried to like tridactyl on Firefox but there were too many rough edges and it was unreliable (not really their fault, mainly limitations of what webextensions can do). As a result it was frustrating to have your keyboard shortcuts not work right ~25% of the time because you had the wrong part of the browser focused or something like that.
The main problem I have with it is it does not keep key combinations stable — if you press F → Esc → F → … (or Alt+F), it assigns different combinations for each link each time.