What should I do to make my code for the uniform grid generic ?

Forget it. Future proofing code is the source of all procrastinations (trust me, I am fighting my instinct to do the "smart thing" every day :-) ). When you want to write your improved algo you will know better how to adapt and how to change it. No need to write a thesis about ray intersection abstraction or bit pattern matches. The code used in production renderers using octrees and sparse voxel octrees (whih I think are just a fad and so does John Carmack ;-) ) is so human unreadable that it hurts the eyes. It's layers of hack on hack of bit pattern shifts and masks that you won't know what is going on.

Long story short. Just implement what you have and think of speed and other data structures later.