Hello!

I've been planning to start a new game for a while now, but I'm unsure about the mentioned mods.

How compatible are they with TR and NoM? Which one do YOU prefer?

I prefer Wakims. I find BTB's mod to be a little heavy handed in disabling spell making and enchanting and in general it just goes too far for my tastes. If what you want is to gimp yourself as much as possible so the game will still be hard at high level, then go with BTB. If you want to make the game a little harder while preserving more roleplay options then I'd go with Wakims.

I have Wakims and TR in my load order and have not noticed any issues, although I have not explored greatly in the new areas added by TR.

I have no experience with NOM.