Should we add a base to water, or do the reverse?
You are adding to a solid to a liquid (or vice versa). I don't think the order of addition is too important.............
You know the order of addition is important in the addition of acid to water. Why? Because if you spit in acid, it spits back at you. And so you don't spit in the acid, and DON'T add water to the acid, and
With bases, I tended to weigh out a mass of sodium hydroxide or potassium hydroxide, and THEN added a bit of water (i.e not the full volume). The solution (the lye) WOULD get hot, but the heat tended to bring all the solute into solution, and then you could dilute to the full, required volume of liquid when ALL of the solute had gone up. When you add solid bases to bulk volumes of water, I found that they tended to be reluctant to go up completely.
But remember what I said with regard to acid: it is