Recently, when I was at the conference, a classmate of mine asked my about the meaning of nothing and we had the discussion about this. Since I know a kit of Japanese, we ended up discussing what kind of kanji is used for nothing. I imagined that the one used is most likely 無, but I was not sure and I had no idea what kind of concepts and ideas were incorporated in it, so I decided to research it a bit.
A quick search at the Japanese-English dictionary gave me three possible candidates: 無, 空, and 虚.
The character 無 is used in the words like 無い, which is used as negation of the sentence, 無くす, in the meaning of losing, 無限 as the infinite, 無理, as in impossible, 無効 as invalid, and 無駄 as useless. The radical that is used to search for is actually 火, which are the four dots at the bottom.
Looking at the history of the character, it seems that at first it was used to indicate the dancing. Which does not make a lot of sense conceptually, but looking at the character, it is a little more clear. Comparing 無 and 舞, they have the same upper part with something at the bottom. Just that instead of the fire (火) it has the opposite (舛) as the bottom part.
Beside the fire (火), the part that is also used in this character is 40 (卌), but it can also be multitude. There are also characters, that use it as part of them. Some of them are creasing (撫でる), type of vegetables (蕪) and being certain (嘸かし).
The second character 空 can mean both the sky and empty. It first meaning was the sky, and it only latter expanded to include empty. But it seems that one of the older meanings of the character was also hole. It is used in words like 空 sky, 空港 airport, 空気 air, 空き space, 空っぽ empty, and so on.
The radical for this is 穴, meaning cave. Looking from the history of the character, it is created from the character of hole (穴) and phonetic part with the meaning of construction or skill (工). But in this particular kanji, the 工 also have the meaning of the curve, indicating the effect of seeing the horizon as the curve, because the Earth is round.
Some other characters that include this character as their part are harp (箜篌), cavity (腔), waiting/restraining (控える) and urgent (倥偬).
There is also 虚, but the only pace I have seen it so Bleach manga, so I am not going to analyze it. It is part of the kanji for lying (嘘), or at least it looks very similar.
This helped my to get some sort of sense or intuition of what these characters mean. But this still does not help me figure out which one would be be better suited. Thankfully, this question on the Japanese StackExchenge is providing some pointers to it.
Based on this answer, it seems like 無 means a complete absence of anything, while 空 refers to emptiness, like the emptiness of the air (back when they still believed that air was empty) or emptiness of the cup.
Another answer indicates that there is a difference in Buddhism and Daoism that is responsible for this. The Daoism uses is as nothing, like not existing, not being able to define it or pragmatical emptiness as in empty room to non-intentionality. It refers to non-descriptivity of things.
On the other hand, in Buddhism the term is a translation of 'sunyata' or emptiness. I refers to the belief that there is noting constant or permanent. So they are somehow similar in their conceptualization. But in order to distinguish them, the Buddhism used the 空, while the Daoism used 無.
So, now if I need to understand which one is more relevant (so far I am leaning towards 無), I need to study both concepts in Buddhism and Daoism? I think I am going to stop here, as I am not the one that is interesting in this concept.